Author: Felix Hausdorff

Publisher: American Mathematical Soc.

ISBN: 082840061X

Release Date: 1949-01-01

Genre: Mathematics

This reprint of the original 1914 edition of this famous work contains many topics that had to be omitted from later editions, notably, Symmetric Sets, Principle of Duality, most of the ``Algebra'' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, the Special Methods Applicable in the Euclidean Plane, Jordan's Separation Theorem, the Theory of Content and Measure, the Theory of the Lebesgue Integral. The text is in German.
## The Foundations of Mathematics

## Handbook of Mathematical Logic

## Foundations of Set Theory

## Set Theory An Introduction To Independence Proofs

## Naive Mengenlehre

## Problems in the Philosophy of Mathematics

## Abstract set theory

## Harvey Friedman s Research on the Foundations of Mathematics

## Foundational Studies

## Handbook of mathematical logic

## An Introduction to Mathematical Logic and Type Theory

Author: Peter B. Andrews

Publisher: Springer Science & Business Media

ISBN: 1402007639

Release Date: 2002-07-31

Genre: Computers

In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Publisher: Springer Science & Business Media

ISBN: 1402007639

Release Date: 2002-07-31

Genre: Computers