First Order Mathematical Logic

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First Order Mathematical Logic

Author : Angelo Margaris
Publisher : Courier Corporation
ISBN 13 : 9780486662695
Total Pages : 244 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis First Order Mathematical Logic by : Angelo Margaris

Download or read book First Order Mathematical Logic written by Angelo Margaris and published by Courier Corporation. This book was released on 1990-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews

First-Order Logic

Author : Raymond R. Smullyan
Publisher : Springer Science & Business Media
ISBN 13 : 3642867189
Total Pages : 167 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis First-Order Logic by : Raymond R. Smullyan

Download or read book First-Order Logic written by Raymond R. Smullyan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. We use the term "analytic" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as "analysing" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term "Boolean valuation" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).

Mathematical Logic

Author : H.-D. Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 1475723555
Total Pages : 290 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Mathematical Logic by : H.-D. Ebbinghaus

Download or read book Mathematical Logic written by H.-D. Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Extensions of First-Order Logic

Author : Maria Manzano
Publisher : Cambridge University Press
ISBN 13 : 9780521354356
Total Pages : 414 pages
Book Rating : 4.3/5 (543 download)

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Book Synopsis Extensions of First-Order Logic by : Maria Manzano

Download or read book Extensions of First-Order Logic written by Maria Manzano and published by Cambridge University Press. This book was released on 1996-03-29 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.

Mathematical Logic

Author : Stephen Cole Kleene
Publisher : Courier Corporation
ISBN 13 : 0486317072
Total Pages : 416 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Mathematical Logic by : Stephen Cole Kleene

Download or read book Mathematical Logic written by Stephen Cole Kleene and published by Courier Corporation. This book was released on 2013-04-22 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Introduction to Mathematical Logic

Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
ISBN 13 : 1461572886
Total Pages : 351 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Introduction to Mathematical Logic by : Elliot Mendelsohn

Download or read book Introduction to Mathematical Logic written by Elliot Mendelsohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.

Fundamentals of Mathematical Logic

Author : Peter G. Hinman
Publisher : CRC Press
ISBN 13 : 1439864276
Total Pages : 894 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Fundamentals of Mathematical Logic by : Peter G. Hinman

Download or read book Fundamentals of Mathematical Logic written by Peter G. Hinman and published by CRC Press. This book was released on 2018-10-08 with total page 894 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

An Introduction to Mathematical Logic

Author : Richard E. Hodel
Publisher : Courier Corporation
ISBN 13 : 0486497852
Total Pages : 514 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis An Introduction to Mathematical Logic by : Richard E. Hodel

Download or read book An Introduction to Mathematical Logic written by Richard E. Hodel and published by Courier Corporation. This book was released on 2013-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

A Beginner's Guide to Mathematical Logic

Author : Raymond M. Smullyan
Publisher : Courier Corporation
ISBN 13 : 0486782972
Total Pages : 304 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis A Beginner's Guide to Mathematical Logic by : Raymond M. Smullyan

Download or read book A Beginner's Guide to Mathematical Logic written by Raymond M. Smullyan and published by Courier Corporation. This book was released on 2014-03-19 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining stories of great writers and philosophers with quotations and riddles, this completely original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2013 edition.

Metalogic

Author : Geoffrey Hunter
Publisher : Univ of California Press
ISBN 13 : 9780520023567
Total Pages : 306 pages
Book Rating : 4.0/5 (235 download)

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Book Synopsis Metalogic by : Geoffrey Hunter

Download or read book Metalogic written by Geoffrey Hunter and published by Univ of California Press. This book was released on 1973-06-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Included is a complete proof, accessible to non-mathematicians, of the undecidability of first order logic, the most important fact about logic to emerge from the work of the last half-century. Hunter explains concepts of mathematics and set theory along the way for the benefit of non-mathematicians. He also provides ample exercises with comprehensive answers.

First Course in Mathematical Logic

Author : Patrick Suppes
Publisher : Courier Corporation
ISBN 13 : 0486150941
Total Pages : 308 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis First Course in Mathematical Logic by : Patrick Suppes

Download or read book First Course in Mathematical Logic written by Patrick Suppes and published by Courier Corporation. This book was released on 2012-04-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.

The Foundations of Mathematics

Author : Kenneth Kunen
Publisher :
ISBN 13 : 9781904987147
Total Pages : 251 pages
Book Rating : 4.9/5 (871 download)

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Book Synopsis The Foundations of Mathematics by : Kenneth Kunen

Download or read book The Foundations of Mathematics written by Kenneth Kunen and published by . This book was released on 2009 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

First Order Categorical Logic

Author : M. Makkai
Publisher : Springer
ISBN 13 : 3540371001
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis First Order Categorical Logic by : M. Makkai

Download or read book First Order Categorical Logic written by M. Makkai and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

First-Order Modal Logic

Author : M. Fitting
Publisher : Springer Science & Business Media
ISBN 13 : 9401152926
Total Pages : 300 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis First-Order Modal Logic by : M. Fitting

Download or read book First-Order Modal Logic written by M. Fitting and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Metamathematics of First-Order Arithmetic

Author : Petr Hájek
Publisher : Cambridge University Press
ISBN 13 : 1107168414
Total Pages : 475 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Metamathematics of First-Order Arithmetic by : Petr Hájek

Download or read book Metamathematics of First-Order Arithmetic written by Petr Hájek and published by Cambridge University Press. This book was released on 2017-03-02 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

A Friendly Introduction to Mathematical Logic

Author : Christopher C. Leary
Publisher : Lulu.com
ISBN 13 : 1942341075
Total Pages : 382 pages
Book Rating : 4.9/5 (423 download)

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Book Synopsis A Friendly Introduction to Mathematical Logic by : Christopher C. Leary

Download or read book A Friendly Introduction to Mathematical Logic written by Christopher C. Leary and published by Lulu.com. This book was released on 2015 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

First-Order Logic and Automated Theorem Proving

Author : Melvin Fitting
Publisher : Springer Science & Business Media
ISBN 13 : 1468403575
Total Pages : 258 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis First-Order Logic and Automated Theorem Proving by : Melvin Fitting

Download or read book First-Order Logic and Automated Theorem Proving written by Melvin Fitting and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.