[PDF] Sets Logic Computation An Open Introduction To Metalogic eBook

Author : Richard Zach
Publisher :
Page : pages
File Size : 17,73 MB
Release : 2019
Category : Electronic books
ISBN :

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Sets, Logic, Computation is an introductory textbook on metalogic. 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. The audience is undergraduate students with some background in formal logic, e.g., what is covered by forall x. NOTE: It's title has been changed from "Sets, Logic, Computation: An Open Logic Text" to "Sets, Logic, Computation: An Open Introduction to Metalogic."

Author : Richard Zach
Publisher :
Page : 418 pages
File Size : 41,71 MB
Release : 2021-07-13
Category :
ISBN :

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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.

Author : Richard Zach
Publisher :
Page : 360 pages
File Size : 10,9 MB
Release : 2017
Category : Electronic books
ISBN :

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"This textbook is based on the Open Logic Project. 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"--BCcampus website.

Author : Geoffrey Hunter
Publisher : Univ of California Press
Page : 306 pages
File Size : 24,1 MB
Release : 1973-06-26
Category : Mathematics
ISBN : 9780520023567

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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.

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 39,98 MB
Release : 2004-01-15
Category : Philosophy
ISBN : 0191556432

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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Author : George S. Boolos
Publisher : Cambridge University Press
Page : 365 pages
File Size : 21,27 MB
Release : 2007-09-17
Category : Computers
ISBN : 0521877520

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This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.

Author : Christopher C. Leary
Publisher : Lulu.com
Page : 382 pages
File Size : 23,68 MB
Release : 2015
Category : Education
ISBN : 1942341075

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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.

Author : Richard Zach
Publisher : Createspace Independent Publishing Platform
Page : 228 pages
File Size : 12,88 MB
Release : 2017-06-15
Category :
ISBN : 9781548138080

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A textbook on recursive function theory and G�del's incompleteness theorems. Also covers models of arithmetic and second-order logic.

Author : Paolo Mancosu
Publisher : Oxford University Press
Page : 431 pages
File Size : 44,77 MB
Release : 2021
Category : Philosophy
ISBN : 0192895931

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An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.