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.
New Foundations in Mathematics
New Foundations in 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 New Foundations in Mathematics write by Garret Sobczyk. This book was released on 2012-10-26. New Foundations in Mathematics available in PDF, EPUB and Kindle. The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Conceptions of Set and the Foundations of Mathematics
Conceptions of Set 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 Conceptions of Set and the Foundations of Mathematics write by Luca Incurvati. This book was released on 2020-01-23. Conceptions of Set and the Foundations of Mathematics available in PDF, EPUB and Kindle. Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
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.
