Fundamentals of Mathematical Logic PDF Download
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Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Category : Mathematics
Languages : en
Pages : 894
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Book Description
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.
Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Category : Mathematics
Languages : en
Pages : 894
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Book Description
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.
Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486782972
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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.
Author: H.-D. Ebbinghaus
Publisher: Springer Science & Business Media
ISBN: 1475723555
Category : Mathematics
Languages : en
Pages : 290
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Book Description
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.
Author: Abram Aronovich Stolyar
Publisher: Courier Corporation
ISBN: 0486645614
Category : Mathematics
Languages : en
Pages : 229
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Book Description
This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. 1970 edition.
Author: Yves Nievergelt
Publisher: Springer Science & Business Media
ISBN: 146120125X
Category : Mathematics
Languages : en
Pages : 425
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Book Description
This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Author: George E. Owen
Publisher: Courier Corporation
ISBN: 0486164586
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.
Author: Herbert B. Enderton
Publisher: Elsevier
ISBN: 0080496466
Category : Computers
Languages : en
Pages : 330
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Book Description
A Mathematical Introduction to Logic
Author: Elliot Mendelsohn
Publisher: Springer Science & Business Media
ISBN: 1461572886
Category : Science
Languages : en
Pages : 351
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Book Description
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.
Author: Wolfgang Rautenberg
Publisher: Springer Science & Business Media
ISBN: 0387342419
Category : Mathematics
Languages : en
Pages : 273
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Book Description
While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.
Author: Yu.I. Manin
Publisher: Springer Science & Business Media
ISBN: 1475743858
Category : Mathematics
Languages : en
Pages : 296
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Book Description
1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.
