Foundational Aspects of "Non"standard Mathematics

Foundational Aspects of "Non"standard Mathematics - Contemporary Mathematics

Paperback (30 Nov 1994)

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Publisher's Synopsis

This work proposes a major new extension of 'non' standard mathematics. Addressed to a general mathematical audience, the book is intended to be philosophically provocative. The model theory on which 'non' standard mathematics has been based is first reformulated within point set topology, which facilitates proofs and adds perspective. These topological techniques are then used to give new, uniform conservativity proofs for the various versions of 'non'standard mathematics proposed by Nelson, Hrbacek, and Kawai.The proofs allow for sharp comparison. Addressing broader issues, Ballard then argues that what is novel in these forms of 'non'standard mathematics is the introduction, however tentative, of relativity in one's mathematical environment. This hints at the possibility of a mathematical environment which is radically relativistic. The work's major and final feature is to present and prove conservative a version of 'non'standard mathematics which, for the first time, illustrates this full radical relativism. The book is entirely self-contained, with all necessary background in point set topology, model theory, 'non'standard analysis, and set theory provided in full.

Book information

ISBN: 9780821802939
Publisher: American Mathematical Society
Imprint: American Mathematical Society
Pub date:
DEWEY: 511.2
DEWEY edition: 20
Language: English
Number of pages: 135
Weight: 257g
Height: 230mm
Width: 171mm
Spine width: 12mm