At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites. Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory.
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The aim of this paper is to derive a nonstandard flat integral representation for certain stable type Euclidean random field measures. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constructive ordered fields, regular formal topologies, regular formal topology, constructive nonstandard analysis, positive linear order, positive partial order, constructive linear order, nonlogical rules, random field measures, constructive measure theory, nonstandard arguments, nonstandard proof, apartness relation, strong extensionality, game induction, countable choice, weak partial order, standard part map, recursive measure, lattice axioms, bar induction, syzygy theorem, positive lattices, synthetic differential geometry, strict linear order Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reuniting the Antipodes, Kluwer Academic Publishers, New York, Douglas Bridges, Lecture Notes, Fred Richman, Principle of Excluded Middle, Academic Press, Symbolic Logic, Peter Schuster, Computer Science, London Math, Mathematical Subject Classification, Errett Bishop, North Holland, Principle of Bivalence, New Zealand, Principle of Contradiction, Locale Theory, Paul Lorenzen, Rhode Island New!
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The aim of this paper is to derive a nonstandard flat integral representation for certain stable type Euclidean random field measures. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constructive ordered fields, regular formal topologies, regular formal topology, constructive nonstandard analysis, positive linear order, positive partial order, constructive linear order, nonlogical rules, random field measures, constructive measure theory, nonstandard arguments, nonstandard proof, apartness relation, strong extensionality, game induction, countable choice, weak partial order, standard part map, recursive measure, lattice axioms, bar induction, syzygy theorem, positive lattices, synthetic differential geometry, strict linear order Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reuniting the Antipodes, Kluwer Academic Publishers, New York, Douglas Bridges, Lecture Notes, Fred Richman, Principle of Excluded Middle, Academic Press, Symbolic Logic, Peter Schuster, Computer Science, London Math, Mathematical Subject Classification, Errett Bishop, North Holland, Principle of Bivalence, New Zealand, Principle of Contradiction, Locale Theory, Paul Lorenzen, Rhode Island New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
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This book cites 100
books:
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- Midwest Studies in Philosophy: Philosophy of Science by Peter A. French on 6 pages
- Constructive Analysis (Grundlehren Der Mathematischen Wissenschaften) by Errett Bishop on 5 pages
- Non-standard Analysis by Abraham Robinson on page 165, and page 166
- Philosophy of Science (Paragon Issues in Philosophy) by James Fetzer in Back Matter (1), and Back Matter (2)
- On Numbers and Games by John H. Conway on page 211, and page 226
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