14 found
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  1. Standard foundations for nonstandard analysis.David Ballard & Karel Hrbacek - 1992 - Journal of Symbolic Logic 57 (2):741-748.
  2.  18
    Infinitesimal analysis without the Axiom of Choice.Karel Hrbacek & Mikhail G. Katz - 2021 - Annals of Pure and Applied Logic 172 (6):102959.
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  3.  21
    Realism, nonstandard set theory, and large cardinals.Karel Hrbacek - 2001 - Annals of Pure and Applied Logic 109 (1-2):15-48.
    Mathematicians justify axioms of set theory “intrinsically”, by reference to the universe of sets of their intuition, and “extrinsically”, for example, by considerations of simplicity or usefullness for mathematical practice. Here we apply the same kind of justifications to Nonstandard Analysis and argue for acceptance of BNST+ . BNST+ has nontrivial consequences for standard set theory; for example, it implies existence of inner models with measurable cardinals. We also consider how to practice Nonstandard Analysis in BNST+, and compare it with (...)
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  4.  14
    On the Complexity of Analytic Sets.Karel Hrbacek - 1978 - Mathematical Logic Quarterly 24 (25‐30):419-425.
  5.  23
    On the Complexity of Analytic Sets.Karel Hrbacek - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):419-425.
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  6.  64
    Standard sets in nonstandard set theory.Petr Andreev & Karel Hrbacek - 2004 - Journal of Symbolic Logic 69 (1):165-182.
    We prove that Standardization fails in every nontrivial universe definable in the nonstandard set theory BST, and that a natural characterization of the standard universe is both consistent with and independent of BST. As a consequence we obtain a formulation of nonstandard class theory in the ∈-language.
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  7.  14
    Combinatorial principles in nonstandard analysis.Mauro Di Nasso & Karel Hrbacek - 2003 - Annals of Pure and Applied Logic 119 (1-3):265-293.
    We study combinatorial principles related to the isomorphism property and the special model axiom in nonstandard analysis.
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  8.  19
    A New Proof that π 11 < σ 11.Richard Gostanian & Karel Hrbacek - 1979 - Mathematical Logic Quarterly 25 (25‐29):407-408.
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  9.  27
    A New Proof that π11 < σ11.Richard Gostanian & Karel Hrbacek - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):407-408.
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  10.  7
    Constructing Nonstandard Hulls and Loeb Measures in Internal Set Theories.Karel Hrbacek & Mikhail G. Katz - 2023 - Bulletin of Symbolic Logic 29 (1):97-127.
    Currently the two popular ways to practice Robinson’s nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions relying on external sets. We show that internal frameworks provide successful accounts of nonstandard hulls and Loeb measures. The basic fact this work relies on is that the ultrapower of the standard universe by a standard ultrafilter is naturally isomorphic to a subuniverse of the internal universe.
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  11.  13
    Degrees of analytic sets.Karel Hrbacek - 1983 - Mathematical Logic Quarterly 29 (2):75-82.
  12.  21
    On the Existence of Two Analytic Non-Borel Sets Which are not Isomorphic.A. Maitra, C. Ryll-Nardzewski, R. Daniel Mauldin, Karel Hrbacek & Stephen G. Simpson - 1984 - Journal of Symbolic Logic 49 (2):665-668.
  13.  7
    Review: Vladimir Kanovei, Michael Reeken, Internal Approach to External Sets and Universes. Part 1. Bounded Set Theory; Vladimir Kanovei, Michael Reeken, Internal Approach to External Sets and Universes. Part 2. External Universe over the Universe of Bounded Set Theory; Vladimir Kanovei, Michael Reeken, Internal Approach to External Sets and Universes. Part 3. Partially Saturated Universes. [REVIEW]Karel Hrbacek - 1999 - Journal of Symbolic Logic 64 (3):1365-1366.
  14.  20
    Vladimir Kanovei and Michael Reeken, Internal approach to external sets and universes, Part 1, Bounded set theory, Studia logica, vol. 55 , pp. 229–257. - Vladimir Kanovei and Michael Reeken, Internal approach to external sets and universes, Part 2, External universes over the universe of bounded set theory, Studia logica, vol. 55 , pp. 347–376. - Vladimir Kanovei and Michael Reeken, Internal approach to external sets and universes, Part 3, Partially saturated universes, Studia logica, vol. 56 , pp. 293–322. [REVIEW]Karel Hrbacek - 1999 - Journal of Symbolic Logic 64 (3):1365-1366.
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