The Foundations of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Foundations of Mathematics write by Kenneth Kunen. This book was released on 2009. The Foundations of Mathematics available in PDF, EPUB and Kindle. 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.
The Logical Foundations of Mathematics
The Logical Foundations of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Logical Foundations of Mathematics write by William S. Hatcher. This book was released on 2014-05-09. The Logical Foundations of Mathematics available in PDF, EPUB and Kindle. 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.
Introduction to the Foundations of Mathematics
Introduction to the Foundations of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to the Foundations of Mathematics write by Raymond L. Wilder. This book was released on 2013-09-26. Introduction to the Foundations of Mathematics available in PDF, EPUB and Kindle. Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
The Foundations of Mathematics in the Theory of Sets
The Foundations of Mathematics in the Theory of Sets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Foundations of Mathematics in the Theory of Sets write by John P. Mayberry. This book was released on 2000. The Foundations of Mathematics in the Theory of Sets available in PDF, EPUB and Kindle. This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Kurt Gödel and the Foundations of Mathematics
Kurt Gödel and the Foundations of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Kurt Gödel and the Foundations of Mathematics write by Matthias Baaz. This book was released on 2011-06-06. Kurt Gödel and the Foundations of Mathematics available in PDF, EPUB and Kindle. This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
