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| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Alonzo Church, 1996 A classic account of mathematical logic from a pioneering giant in the field Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979. At his death in 1995, Church was still regarded as the greatest mathematical logician in the world. |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Alonzo Church, 1944 |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic, by Alonzo Church Alonzo Church, 1956 |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic, V1 Alonzo Church, 2013-03 |
| alonzo church introduction to mathematical logic: A Friendly Introduction to Mathematical Logic Christopher C. Leary, Lars Kristiansen, 2015 At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises. |
| alonzo church introduction to mathematical logic: Notes of Alonzo Church's "Introduction to Mathematical Logic". John Lacey Harvey, 1947 |
| alonzo church introduction to mathematical logic: A Mathematical Introduction to Logic Herbert B. Enderton, 2001-01-23 A Mathematical Introduction to Logic |
| alonzo church introduction to mathematical logic: The Collected Works of Alonzo Church Tyler Burge, Herbert Enderton, 2019-04-23 Writings, including articles, letters, and unpublished work, by one of the twentieth century's most influential figures in mathematical logic and philosophy. Alonzo Church's long and distinguished career in mathematics and philosophy can be traced through his influential and wide-ranging writings. Church published his first article as an undergraduate at Princeton in 1924 and his last shortly before his death in 1995. This volume collects all of his published articles, many of his reviews, his monograph The Calculi of Lambda-Conversion, the introduction to his important and authoritative textbook Introduction to Mathematical Logic, a substantial amount of previously unpublished work (including chapters for the unfinished second volume of Introduction to Mathematical Logic), and a selection of letters to such correspondents as Rudolf Carnap and W. V. O. Quine. With the exception of the reviews, letters, and unpublished work, these appear in chronological order, for the most part in the format in which they were originally published. Church's work in calculability, especially the monograph on the lambda-calculus, helped lay the foundation for theoretical computer science; it attracted the interest of Alan Turing, who later completed his PhD under Church's supervision. (Church coined the term “Turing machine” in a review.) Church's influential textbook, still in print, defined the field of mathematical logic for a generation of logicians. In addition, his close connection with the Association for Symbolic Logic and his many years as review editor for the Journal of Symbolic Logic are documented in the reviews included here. |
| alonzo church introduction to mathematical logic: Alonzo Church, Introduction to mathematical logic, Vol. 1 Heinrich Scholz, 1957 |
| alonzo church introduction to mathematical logic: Alan Turing's Systems of Logic Alan Mathison Turing, 2014-11-16 A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that mathematical reasoning can be done, and should be done, in mechanizable formal logic. Turing's vision of constructive systems of logic for practical use has become reality: in the twenty-first century, automated formal methods are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science. |
| alonzo church introduction to mathematical logic: Principia Mathematica Alfred North Whitehead, Bertrand Russell, 1927 The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century. |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Jayant Ramaswamy, 2025-02-20 Introduction to Mathematical Logic is tailored for undergraduate students seeking a comprehensive introduction to this essential field of mathematics. We provide an accessible yet rigorous exploration of the principles, methods, and applications of mathematical logic. From the foundations of propositional and predicate logic to advanced topics like Gödel's incompleteness theorems and computability theory, we cover a broad range of concepts central to the study of logic. Through clear explanations, illustrative examples, and carefully crafted exercises, students will develop a deep understanding of logical reasoning, formal proof techniques, and the structure of mathematical arguments. Moreover, we emphasize the interdisciplinary nature of mathematical logic, showcasing its relevance in mathematics, philosophy, computer science, and beyond. Real-world applications of logical reasoning are woven throughout the text, demonstrating how logical principles underpin various fields of study, from algorithm design and formal verification to philosophical analysis and linguistic theory. Whether you're a mathematics major, a philosophy student, or pursuing studies in computer science, this book equips you with the tools and insights necessary to navigate the complexities of mathematical logic with confidence. With its blend of theory and application, this text serves as an invaluable resource for undergraduate students embarking on their journey into the realm of mathematical logic. |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Thinking Friedrich Waismann, 2012-08-07 Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition. |
| alonzo church introduction to mathematical logic: An Introduction to Functional Programming Through Lambda Calculus Greg Michaelson, 2013-04-10 Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition. |
| alonzo church introduction to mathematical logic: Introduction to Metamathematics S.C. Kleene, 1980-01-01 Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gadel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which nothing was ever the same. Kleene was an important figure in logic, and lived a long full life of scholarship and teaching. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gade1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Gadel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education. |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Micha? Walicki, 2012 This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book does not presuppose any previous knowledge and can be used also for self-study by more ambitious students. Starting with the basics of set theory, induction and computability, it covers propositional and first-order logic their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts. Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules of a high, though often neglected, pedagogical value aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers. An overview of the history of logic precedes the main text, in which careful presentation of concepts, results and examples is accompanied by the informal analogies and illustrations. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of mathematical logic. |
| alonzo church introduction to mathematical logic: An Introduction to Mathematical Logic and Type Theory Peter B. Andrews, 2013-04-17 In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. |
| alonzo church introduction to mathematical logic: Sets, Logic, Computation Richard Zach, 2021-07-13 A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org. |
| alonzo church introduction to mathematical logic: The Gentle Art of Mathematics Dan Pedoe, 2012-12-27 This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more. |
| alonzo church introduction to mathematical logic: Propositional and Predicate Calculus: A Model of Argument Derek Goldrei, 2005-12-27 Designed specifically for guided independent study. Features a wealth of worked examples and exercises, many with full teaching solutions, that encourage active participation in the development of the material. It focuses on core material and provides a solid foundation for further study. |
| alonzo church introduction to mathematical logic: On Formally Undecidable Propositions of Principia Mathematica and Related Systems Kurt Gödel, 1992-01-01 In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite. |
| alonzo church introduction to mathematical logic: Logic Matters P. T. Geach, B. Geach, 1980-04-30 This is a significant and ofren rather demanding collection of essays. It is an anthology purring together the uncollected works of an important twentieth-century philosopher. Many of the articles treat one or another of the more important issues considered by analytic philosophers during the last quarter-century. Of significant importance to philosophers interested in researching the many topics contained in Logic Matters is the inclusion in this anthology of a rather extensive eight-page name-topic index.--Thomist The papers are arranged by topic: Historical Essays, Traditional Logic, Theory of Reference and Syntax, Intentionality, Quotation and Semantics, Set Theory, Identity Theory, Assertion, Imperatives and Practical Reasoning, Logic in Metaphysics and Theology. The broad range of issues that have engaged Geach's complex and systematic reasoning is impressive. In addition to classical logic, topics in ethics, ontology, and even the logic of religious dogmas are tackled .... the work in this collection is more brilliant and ingenious than it is difficult and demanding.--Philosophy of Science Geach displays his mastery of applying logical techniques and concepts to philosophical questions. Compared with most works in philosophical logic this book is remarkable for its range of topics. Plato, Aristotle, Aquinas, Russell, Wittgenstein, and Quine all figure prominently. Geach's style is remarkably lively considering the rightly argued matter. Although some of the articles treat rather technical questions in mathematical logic, most are accessible to philosophers with modest backgrounds in logic. --Choice |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Alonzo Church, 1956 |
| alonzo church introduction to mathematical logic: Einführung in Die Symbolische Logik Rudolf Carnap, 1958-01-01 A clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. It then considers the application of symbolic logic to the clarification and axiomatization of theories in mathematics, physics, and biology. Hundreds of problems, examples, and exercises. 1958 edition. |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Alonzo Church, 1994 |
| alonzo church introduction to mathematical logic: Introduction to mathematical logic , 1970 |
| alonzo church introduction to mathematical logic: Model Theory : An Introduction David Marker, 2006-04-06 Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures |
| alonzo church introduction to mathematical logic: Introduction to Mathematical Logic Alonso Church, 1998 |
| alonzo church introduction to mathematical logic: The Development of Symbolic Logic Arthur Thomas Shearman, 1906 |
| alonzo church introduction to mathematical logic: Logic, Meaning and Computation Alonzo Church, 2001 This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. |
| alonzo church introduction to mathematical logic: Indiscrete Thoughts Gian-Carlo Rota, 2009-11-03 Indiscrete Thoughts gives a glimpse into a world that has seldom been described that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period —Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay “The Pernicious Influence of Mathematics upon Philosophy” (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come. |
| alonzo church introduction to mathematical logic: Laws of Form G. Spencer-Brown, 1972 |
| alonzo church introduction to mathematical logic: Many-valued Logics John Barkley Rosser, Atwell R. Turquette, 1958 |
| alonzo church introduction to mathematical logic: A New Kind of Science Stephen Wolfram, 2018-11-30 NOW IN PAPERBACK€Starting from a collection of simple computer experiments€illustrated in the book by striking computer graphics€Stephen Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. |
| alonzo church introduction to mathematical logic: Subsystems of Second Order Arithmetic Stephen G. Simpson, 2009-05-29 Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic. |
| alonzo church introduction to mathematical logic: Sketches of the New Jersey Historical Society Alonzo Church, 1894 |
| alonzo church introduction to mathematical logic: A First Course in Logic Mark Verus Lawson, 2018-12-07 A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will? Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability. |
| alonzo church introduction to mathematical logic: Proof Theory Katalin Bimbo, 2014-08-20 Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi |
| alonzo church introduction to mathematical logic: Logic in Elementary Mathematics Robert M. Exner, Myron F. Rosskopf, 2011-01-01 This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Topics include axiomatic structure and the relation of theory to interpretation. No prior training in logic is necessary, and numerous examples and exercises aid in the mastery of the language of logic. 1959 edition-- |
| alonzo church introduction to mathematical logic: The New Era in American Mathematics, 1920–1950 Karen Hunger Parshall, 2022-02-22 A meticulously researched history on the development of American mathematics in the three decades following World War I As the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920–1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States. Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline. Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920–1950 shows the way one nation became the focal point for the field. |
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Alonzo - Baby Name Meaning, Origin, and Popularity
Jun 8, 2025 · Alonzo is a boy's name of Spanish, Italian origin meaning "noble, ready". Alonzo is the 512 ranked male name by popularity.
Alonzo - Wikipedia
Alonzo is both a given name and a Spanish surname. Notable people with the name include:
Alonzo Name Meaning, Origin, History, And Popularity
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Alonzo (rappeur) — Wikipédia
Alonzo, né le 25 juillet 1982 à Marseille, dans les Bouches-du-Rhône, est un rappeur, chanteur et auteur-compositeur-interprète franco - comorien. Il commence sa …
