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Foundational aspects of non standard mathematics

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 t...

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Autor principal: Ballard, David
Lenguaje:eng
Publicado: American Mathematical Society 1994
Materias:
Acceso en línea:http://cds.cern.ch/record/2622997
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author Ballard, David
author_facet Ballard, David
author_sort Ballard, David
collection CERN
description 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, Hrbáček, 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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spelling cern-26229972021-04-21T18:47:59Zhttp://cds.cern.ch/record/2622997engBallard, DavidFoundational aspects of non standard mathematicsMathematical Physics and MathematicsThis 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, Hrbáček, 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.American Mathematical Societyoai:cds.cern.ch:26229971994
spellingShingle Mathematical Physics and Mathematics
Ballard, David
Foundational aspects of non standard mathematics
title Foundational aspects of non standard mathematics
title_full Foundational aspects of non standard mathematics
title_fullStr Foundational aspects of non standard mathematics
title_full_unstemmed Foundational aspects of non standard mathematics
title_short Foundational aspects of non standard mathematics
title_sort foundational aspects of non standard mathematics
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2622997
work_keys_str_mv AT ballarddavid foundationalaspectsofnonstandardmathematics