Zobrazeno 1 - 10
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pro vyhledávání: '"Hrbacek, Karel"'
Autor:
Hrbacek, Karel
Model-theoretic frameworks for Nonstandard Analysis depend on the existence of nonprincipal ultrafilters, a strong form of the Axiom of Choice (AC). Hrbacek and Katz, APAL 72 (2021) formulate axiomatic nonstandard set theories SPOT and SCOT that are
Externí odkaz:
http://arxiv.org/abs/2405.00621
Autor:
Hrbacek, Karel, Katz, Mikhail G.
Publikováno v:
Journal of Logic and Analysis 15:6 (2023), 1-19
We provide choiceless proofs using infinitesimals of the global versions of Peano's existence theorem and Osgood's theorem on maximal solutions. We characterize all solutions in terms of infinitesimal perturbations. Our proofs are more effective than
Externí odkaz:
http://arxiv.org/abs/2311.01374
Autor:
Hrbacek, Karel, Katz, Mikhail G.
Publikováno v:
Real Analysis Exchange 48 (2023), no. 2, 365-380
We survey the effective foundations for analysis with infinitesimals developed by Hrbacek and Katz in 2021, and detail some applications. Theories SPOT and SCOT are conservative over respectively ZF and ZF+ADC. The range of applications of these theo
Externí odkaz:
http://arxiv.org/abs/2305.09672
Autor:
Hrbacek, Karel, Katz, Mikhail G.
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 o
Externí odkaz:
http://arxiv.org/abs/2301.00367
Autor:
Akin, Ethan, Hrbacek, Karel
We describe those complete linearly ordered topological spaces $X$ which are homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open interval in $X$. Using countable tail-like ordinals as indices, we build towers of distinct CH
Externí odkaz:
http://arxiv.org/abs/2107.13299
Autor:
Hrbacek, Karel, Katz, Mikhail G.
Publikováno v:
Annals of Pure and Applied Logic 172 (2021), no. 6, 102959
It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom of Choice than traditional elementary analysis. The claim is based on the observation that the hyperreals entail the existence of nonprincipal ultrafilte
Externí odkaz:
http://arxiv.org/abs/2009.04980
Autor:
Hrbacek, Karel
Publikováno v:
Journal of Logic and Analysis 12 5 (2020) 1-6
A. Boudaoud asked whether every unlimited integer is a sum of a limited integer and a product of two unlimited integers. Assuming Dickson's Conjecture, the answer is negative. The erroneous proof of claim (2) on page 5 of the published version is rep
Externí odkaz:
http://arxiv.org/abs/1910.02286
Publikováno v:
In Procedia Structural Integrity 2023 43:209-214
Publikováno v:
In Procedia Structural Integrity 2023 43:136-141