The Logical Foundations of Mathematics is popular PDF and ePub book, written by William S. Hatcher in 2014-05-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Logical Foundations of Mathematics can be Read Online from any device for your convenience.
The Logical Foundations of Mathematics Book PDF Summary
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.
Detail Book of The Logical Foundations of Mathematics PDF
- Author : William S. Hatcher
- Release : 09 May 2014
- Publisher : Elsevier
- ISBN : 9781483189635
- Genre : Mathematics
- Total Page : 331 pages
- Language : English
- PDF File Size : 8,8 Mb
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