Sign In | Not yet a member? | Submit your article
 
Home   Technical   Study   Novel   Nonfiction   Health   Tutorial   Entertainment   Business   Magazine   Arts & Design   Audiobooks & Video Training   Cultures & Languages   Family & Home   Law & Politics   Lyrics & Music   Software Related   eBook Torrents   Uncategorized  

The Foundations of Mathematics (Logic)
The Foundations of Mathematics (Logic)
Date: 22 April 2011, 14:30

Free Download Now     Free register and download UseNet downloader, then you can FREE Download from UseNet.

    Download without Limit " The Foundations of Mathematics (Logic) " from UseNet for FREE!
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.
Related Articles:
Logic  

DISCLAIMER:

This site does not store The Foundations of Mathematics (Logic) on its server. We only index and link to The Foundations of Mathematics (Logic) provided by other sites. Please contact the content providers to delete The Foundations of Mathematics (Logic) if any and email us, we'll remove relevant links or contents immediately.



Comments

Comments (0) All

Verify: Verify

    Sign In   Not yet a member?


Popular searches