A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary
Publisher: Lulu.com
ISBN: 1942341075
Category : Computers
Languages : en
Pages : 382

Book Description
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.

A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary
Publisher:
ISBN: 9780130107053
Category : Computer logic
Languages : en
Pages : 0

Book Description
This user-friENDly introduction to the key concepts of mathematical logic focuses on concepts that are used by mathematicians in every branch of the subject. Using an assessible, conversational style, it approaches the subject mathematically (with precise statements of theorems and correct proofs), exposing readers to the strength and power of mathematics, as well as its limitations, as they work through challenging and technical results. : Structures and Languages. Deductions. Comnpleteness and Compactness. Incompleteness--Groundwork. The Incompleteness Theorems. Set Theory. : For readers in mathematics or related fields who want to learn about the key concepts and main results of mathematical logic that are central to the understanding of mathematics as a whole.

A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary
Publisher:
ISBN:
Category : Computer logic
Languages : en
Pages : 365

Book Description
"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"--Textbook Web page.

An Introduction to Mathematical Logic

Author: Richard E. Hodel
Publisher: Courier Corporation
ISBN: 0486497852
Category : Mathematics
Languages : en
Pages : 514

Book Description
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.

Introduction to Mathematical Logic

Author: Elliot Mendelsohn
Publisher: Springer Science & Business Media
ISBN: 1461572886
Category : Science
Languages : en
Pages : 351

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.

A Mathematical Introduction to Logic

Author: Herbert B. Enderton
Publisher: Elsevier
ISBN: 0080496466
Category : Computers
Languages : en
Pages : 330

Book Description
A Mathematical Introduction to Logic

A Concise Introduction to Mathematical Logic

Author: Wolfgang Rautenberg
Publisher: Springer Science & Business Media
ISBN: 0387342419
Category : Mathematics
Languages : en
Pages : 273

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.

Introduction to Logic

Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486138054
Category : Mathematics
Languages : en
Pages : 340

Book Description
Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.

Mathematical Logic

Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 0486317072
Category : Mathematics
Languages : en
Pages : 436

Book Description
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.

A Profile of Mathematical Logic

Author: Howard DeLong
Publisher: Courier Corporation
ISBN: 0486139158
Category : Mathematics
Languages : en
Pages : 322

Book Description
This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.