The Foundations of Mathematics PDF
By:Kenneth Kunen
Published on 2009 by
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.
This Book was ranked at 2 by Google Books for keyword mathematics symbol.
Book ID of The Foundations of Mathematics's Books is _B_oQQAACAAJ, Book which was written byKenneth Kunenhave ETAG "tZ1rtvNvHAY"
Book which was published by since 2009 have ISBNs, ISBN 13 Code is 9781904987147 and ISBN 10 Code is 1904987141
Reading Mode in Text Status is false and Reading Mode in Image Status is false
Book which have "251 Pages" is Printed at BOOK under CategoryMathematics
Book was written in en
eBook Version Availability Status at PDF is falseand in ePub is false
Book Preview
Download The Foundations of Mathematics PDF Free
Download The Foundations of Mathematics Books Free
Download The Foundations of Mathematics Free
Download The Foundations of Mathematics PDF
Download The Foundations of Mathematics Books
No comments:
Post a Comment