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Nonstandard Analysis, Axiomatically
20041 Getting started.- 2 Elementary real analysis in the nonstandard universe.- 3 Theories of internal sets.- 4 Metamathematics of internal theories.- 5 Definable external sets and metamathematics of HST.- 6 Partially saturated universes and the Power Set problem.- 7 Forcing extensions of the nonstandard universe.- 8 Other nonstandard theories.- 9 ...
Vladimir Kanovei, Michael Reeken
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Singular Traces and Nonstandard Analysis
1995We discuss non trivial singular traces on the compact operators, extending some results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states using tools of non standard analysis.
Albeverio, S +3 more
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2018
Nonstandard analysis is an important application of mathematical logic to the rest of mathematics. Invented in 1960, it provided a long-sought-for rigorous justification for the use of infinitely large and infinitely small (infinitesimal) quantities in the differential and integral calculus, and the first sound canon for manipulating such quantities.
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Nonstandard analysis is an important application of mathematical logic to the rest of mathematics. Invented in 1960, it provided a long-sought-for rigorous justification for the use of infinitely large and infinitely small (infinitesimal) quantities in the differential and integral calculus, and the first sound canon for manipulating such quantities.
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Second-order Non-nonstandard Analysis
Studia Logica, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2001
Classical or standard analysis is mostly concerned with the study of the real numbers and with the properties of functions defined on them. We shall now describe the use of the hyperreals as valuable tools for mathematical analysis. Through the existence of infinitesimals, finite, and infinite numbers, NSA provides us with a rich structure which we use
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Classical or standard analysis is mostly concerned with the study of the real numbers and with the properties of functions defined on them. We shall now describe the use of the hyperreals as valuable tools for mathematical analysis. Through the existence of infinitesimals, finite, and infinite numbers, NSA provides us with a rich structure which we use
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The American Mathematical Monthly, 1973
[no abstract] ; © 1973 Mathematical Association of America. Work on this paper was also supported in part by Grant No. GP-7691 from the National Science Foundation.
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[no abstract] ; © 1973 Mathematical Association of America. Work on this paper was also supported in part by Grant No. GP-7691 from the National Science Foundation.
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1997
In this article we show how a nonstandard extension *ℝ of ℝ. can be used to formulate the fundamental ideas of infinitesimal calculus in a natural and intuitive way, and thereby develop real analysis rigorously based on these ideas. We include a number of exercises (which include proofs of results that are only slight developments of the theory) and ...
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In this article we show how a nonstandard extension *ℝ of ℝ. can be used to formulate the fundamental ideas of infinitesimal calculus in a natural and intuitive way, and thereby develop real analysis rigorously based on these ideas. We include a number of exercises (which include proofs of results that are only slight developments of the theory) and ...
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