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.
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
Gewicht
ISBN-13
978-0-8218-0293-9 (9780821802939)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Introduction Part 1. Preliminaries: Point set topology Model theory "Non"standard analysis Part 2. Topological aspects: Introduction Theory of CL spaces Topological determinacy of local internal domains Topological determinacy of internal domains Part 3. Set theoretic aspects: Introduction Standard set theory Current "non"standard set theories Proofs of conservativity Critical review with proposal: EST Conservativity of EST Concluding remarks References Index Symbols.
