The Logical Foundations of Mathematics PDF
By:William S. Hatcher
Published on 2014-05-09 by Elsevier
The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a |natural deduction| style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.
This Book was ranked at 19 by Google Books for keyword mathematics about sets.
Book ID of The Logical Foundations of Mathematics's Books is wf3iBQAAQBAJ, Book which was written byWilliam S. Hatcherhave ETAG "vX0Qr9qgrUY"
Book which was published by Elsevier since 2014-05-09 have ISBNs, ISBN 13 Code is 9781483189635 and ISBN 10 Code is 1483189635
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Book which have "330 Pages" is Printed at BOOK under CategoryMathematics
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