Foundational Aspects of "Non" Standard Mathematics (Contemporary Mathematics) by David Ballard

Other | Science & Mathematics
Foundational Aspects of "Non" Standard Mathematics (Contemporary Mathematics)
Title:
Foundational Aspects of "Non" Standard Mathematics (Contemporary Mathematics)
Author:
David Ballard
ISBN:
0821802933
ISBN13:
978-0821802939
Size PDF:
1294 kb
Size epub:
1551 kb
Publisher:
Amer Mathematical Society (October 1, 1994)
Language:
English
Other formats:
pdf, odf, mobi, cb7, azw, lit, ibooks
Rating:
3.6
Votes:
371

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.

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