KAREL HRBACEK
PUBLICATIONS on Nonstandard Set Theory
Books
with O. Lessmann and R. O’Donovan, Analysis with Ultrasmall
Numbers, CRC Press, Taylor and Francis Group (2015), xxvii + 294
pp.
Articles
Works concerned with the relative (multi-level) approach are marked
with an asterisk.
[1] Axiomatic foundations for nonstandard analysis, Fundamenta
Mathematicae, 98 (1978), 1-19; abstract in J. Symbolic Logic 41 (1976),
285.
[2] Nonstandard set theory, Amer. Math. Monthly, 86 (1979), 659-
677.
https://doi.org/10.2307/2321294
[3] (with D. Ballard) Standard foundations for nonstandard analysis,
Journ. of Symbolic Logic 57, 2 (1992), 741-748.
[4] Realism, nonstandard set theory, and large cardinals, Annals of
Pure and Appl. Logic 109 (2001), 15 - 48.
[5] (with M. Di Nasso) Combinatorial Principles in Nonstandard
Analysis, Annals of Pure and Appl. Logic 119 (2003), 265 - 293.
[6] (with P. Andreev) Standard sets in nonstandard set theory, Journ.
of Symbolic Logic 69 (2004), 165 - 182.
https://doi.org/10.2178/jsl/1080938835
[*7] Internally iterated ultrapowers, in: Nonstandard Models of Arith-
metic and Set Theory, ed. by A. Enayat and R. Kossak, Contemporary
Math. 361, American Mathematical Society, Providence, R.I., 2004, 87
- 120.
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2 KAREL HRBACEK
[8] Some remarks on nonstandard theory of classes, Proceedings of
the International Conference ”Geometric Topology, Discrete Geometry,
and Set Theory,” Moscow, August 24 - 28, 2004, Fundamental and
Applied Mathematics, 11, 5, 2005, 233 - 255.
https://doi.org/10.1007/s10958-007-0374-0
[9] Nonstandard objects in set theory, in: Nonstandard Methods and
Applications in Mathematics, ed. by N. J. Cutland, M. Di Nasso and
D. A. Ross, Lecture Notes in Logic 25, Association for Symbolic Logic,
2006, 80 120.
[*10] Stratified analysis?, in: The Strength of Nonstandard Analysis
(Imme van den Berg and Vitor Neves, eds.), Springer, 47 - 63, 2007.
[*11] Relative set theory: Internal view, Journ. Logic and Analysis
1:8, 2009, 1 - 108.
https://doi.org/10.4115/jla.2009.1.8
[*12] Relative set theory: Some external issues, Journ. Logic and
Analysis 2:8, 2010, 1 - 37.
https://doi.org/10.4115/jla.2010.2.8
[*13] (with O. Lessmann and R. O’Donovan) Analysis with ultrasmall
numbers, Amer. Math. Monthly 117, 9 (2010), 801 816.
https://doi.org/10.4169/000298910X521661
[14] Axiom of Choice in nonstandard set theory, Journ. Logic and
Analysis 4:9, 2012, 1 - 9. https://doi.org/10.4115/jla.2012.4.8
[*15] Relative set theory: Strong stability, Journ. Logic and Analysis
4:11, 2012, 1 - 24. https://doi.org/10.4115/jla.2012.4.11
[16] (with P. Fletcher, V. Kanovei, M. Katz, C. Lobry, and S. Sanders)
Approaches to analysis with infinitesimals following Robinson, Nelson,
and others, Real Analysis Exchange, 42(2) (2017), 193 - 252.
https://arxiv.org/abs/1703.00425
[17] On factoring of unlimited integers, Journ. Logic and Analysis
12:5, 2020, 1 - 6.
https://doi.org/10.48550/arXiv.1910.02286
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[18] (with M. G. Katz) Infinitesimal analysis without the Axiom of
Choice, Ann. Pure Appl. Logic 172, 6 (2021).
https://doi.org/10.1016/j.apal.2021.102959
https://arxiv.org/abs/2009.04980
[19] (with M. G. Katz) Constructing nonstandard hulls and Loeb
measures in internal set theories, Bull. Symb. Logic (2023)
https://arxiv.org/abs/2301.00367
https://doi.org/10.1017/bsl.2022.43
https://doi.org/10.48550/arXiv.2301.00367
