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Descriptive set theory over hyperfinite sets

Published online by Cambridge University Press:  12 March 2014

H. Jerome Keisler ,
Kenneth Kunen ,
Arnold Miller  and
Steven Leth
H. Jerome Keisler
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Kenneth Kunen
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Arnold Miller
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Steven Leth*
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
*
Department of Mathematics, University of Northern Colorado, Greeley, Colorado 80639
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Abstract

The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 4 , December 1989 , pp. 1167 - 1180
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

[C] Cutland, N., A question of Borel hyperdeterminacy, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 30 (1984), pp. 313–316.CrossRefGoogle Scholar
[F] Frankl, P., Families of finite sets satisfying an intersection condition, Bulletin of the Australian Mathematical Society, vol. 15 (1976), pp. 73–79.CrossRefGoogle Scholar
[H1] Henson, C. W., Analytic sets, Baire sets, and the standard part map, Canadian Journal of Mathematics, vol. 31 (1979), pp. 663–672.CrossRefGoogle Scholar
[H2] Henson, C. W., Unbounded Loeb measures, Proceedings of the American Mathematical Society, vol. 74 (1979), pp. 143–150.CrossRefGoogle Scholar
[H3] Henson, C. W., The isomorphism property in nonstandard analysis and its use in the theory of Banach spaces, this Journal, vol. 39 (1974), pp. 717–731.Google Scholar
[HR] Henson, C. W. and Ross, D. (to appear).Google Scholar
[JR] Jayne, J. E. and Rogers, G. A., κ-analytic sets, Analytic sets, Academic Press, New York, 1980, pp. 1–175.Google Scholar
[KM] KUNEN, K. and Miller, A., Borel and projective sets from the point of view of compact sets, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 94 (1983), pp. 399–409.CrossRefGoogle Scholar
[M] Martin, D. A., Descriptive set theory: point classes, Handbook of mathematical logic, North-Holland, Amsterdam, 1977, pp. 783–818.CrossRefGoogle Scholar
[Mi] Mills, C. F., Supercompact spaces and related structures, Ph.D. thesis, University of Wisconsin, Madison, Wisconsin, 1983.Google Scholar
[P] Panetta, R. L., Hyperreal probability spaces: some applications of the Loeb construction, Ph.D. thesis, University of Wisconsin, Madison, Wisconsin, 1978.Google Scholar
[S] Saint-Raymond, J., Fonctions boréliennes sur un quotient, Bulletin des Sciences Mathématiques, ser. 2, vol. 100 (1976), pp. 141–147.Google Scholar
[SB] Stroyan, K. D. and Bayod, J. M., Foundations of infinitesimal stochastic analysis, North-Holland, Amsterdam, 1986.Google Scholar