The Foundations of Mathematics (Studies in Logic: Mathematical

The Foundations of Mathematics (Studies in Logic: Mathematical Logic and Foundations)

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 LÃ¶wenheim-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(Îº) and R(Î³). 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 GÃ¶del, and Tarski's theorem on the non-definability of truth.
Country USA
Brand College Publications
Manufacturer College Publications
Binding Paperback
ItemPartNumber 9114919
Model 9114919
UnitCount 1
EANs 9781904987147
ReleaseDate 0000-00-00

Country	USA
Brand	College Publications
Manufacturer	College Publications
Binding	Paperback
ItemPartNumber	9114919
Model	9114919
UnitCount	1
EANs	9781904987147
ReleaseDate	0000-00-00

The Foundations of Mathematics (Studies in Logic: Mathematical Logic and Foundations)

You might also like...