Sets Models And Proofs PDF Download
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Author | : Ieke Moerdijk |
Publisher | : Springer |
Total Pages | : 141 |
Release | : 2018-11-23 |
Genre | : Mathematics |
ISBN | : 3319924141 |
Download Sets, Models and Proofs Book in PDF, ePub and Kindle
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
Author | : Paolo Mancosu |
Publisher | : Oxford University Press |
Total Pages | : 431 |
Release | : 2021 |
Genre | : Philosophy |
ISBN | : 0192895931 |
Download An Introduction to Proof Theory Book in PDF, ePub and Kindle
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.
Author | : Xavier Caicedo |
Publisher | : CRC Press |
Total Pages | : 474 |
Release | : 1998-11-05 |
Genre | : Mathematics |
ISBN | : 9780824719708 |
Download Models, Algebras, and Proofs Book in PDF, ePub and Kindle
"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide."
Author | : S. Barry Cooper |
Publisher | : Cambridge University Press |
Total Pages | : 450 |
Release | : 1999-06-17 |
Genre | : Mathematics |
ISBN | : 9780521635493 |
Download Sets and Proofs Book in PDF, ePub and Kindle
First of two volumes providing a comprehensive guide to mathematical logic.
Author | : S. Barry Cooper |
Publisher | : Cambridge University Press |
Total Pages | : 433 |
Release | : 1999-06-17 |
Genre | : Computers |
ISBN | : 0521635500 |
Download Models and Computability Book in PDF, ePub and Kindle
Second of two volumes providing a comprehensive guide to the current state of mathematical logic.
Author | : John L. Bell |
Publisher | : Oxford University Press |
Total Pages | : 214 |
Release | : 2011-05-05 |
Genre | : Computers |
ISBN | : 0199609160 |
Download Set Theory Book in PDF, ePub and Kindle
This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.
Author | : Richard H. Hammack |
Publisher | : |
Total Pages | : 314 |
Release | : 2016-01-01 |
Genre | : Mathematics |
ISBN | : 9780989472111 |
Download Book of Proof Book in PDF, ePub and Kindle
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author | : Gilles Dowek |
Publisher | : Springer Science & Business Media |
Total Pages | : 161 |
Release | : 2011-01-11 |
Genre | : Computers |
ISBN | : 0857291211 |
Download Proofs and Algorithms Book in PDF, ePub and Kindle
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
Author | : S. Barry Cooper |
Publisher | : Cambridge University Press |
Total Pages | : 433 |
Release | : 1999-06-17 |
Genre | : Computers |
ISBN | : 0521635500 |
Download Models and Computability Book in PDF, ePub and Kindle
Second of two volumes providing a comprehensive guide to the current state of mathematical logic.
Author | : Jonathan Kirby |
Publisher | : Cambridge University Press |
Total Pages | : 197 |
Release | : 2019-04-18 |
Genre | : Mathematics |
ISBN | : 1316732398 |
Download An Invitation to Model Theory Book in PDF, ePub and Kindle
Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.