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EFFECTIVE CARDINALS OF BOLDFACE POINTCLASSES

ALESSANDRO ANDRETTA

Dipartimento di Matematica, Università di Torino, Italy

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GREG HJORTH

Department of Mathematics, University of California at Los Angeles, USA

Current address: Department of Mathematics and Statistics, University of Melbourne, Australia.

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, and

ITAY NEEMAN

Department of Mathematics, University of California at Los Angeles, USA

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https://doi.org/10.1142/S0219061307000615Cited by:7 (Source: Crossref)

Abstract

Assuming AD + DC(ℝ), we characterize the self-dual boldface pointclasses which are strictly larger (in terms of cardinality) than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank , and those of Wadge rank when ξ is limit.

Keywords:

AMSC: 03E15

References

A. Andretta, Ann. Pure Appl. Log. 123, 162 (2003), DOI: 10.1016/S0168-0072(03)00022-8. Web of Science, Google Scholar
A. Andretta, Ann. Pure Appl. Log. 144, 2 (2006), DOI: 10.1016/j.apal.2006.05.008. Crossref, Web of Science, Google Scholar
G. Hjorth, J. Symb. Log. 63, 663 (1998), DOI: 10.2307/2586857. Crossref, Web of Science, Google Scholar
G. Hjorth, J. Symb. Log. 67, 1351 (2002). Crossref, Web of Science, Google Scholar
J. E. Jayne and C. A. Rogers, J. Math. Pures Appl. 61, 177 (1982). Web of Science, Google Scholar
A. S. Kechris , Classical Descriptive Set Theory , Graduate Texts in Mathematics 156 ( Springer-Verlag , Heidelberg, New York , 1995 ) . Crossref, Google Scholar
J. R. Steel, Determinateness and subsystems of analysis, PhD thesis, University of California, Berkeley (1977) . Google Scholar
R. A. Van Wesep, Subsystems of second-order arithmetic and descriptive set theory under the axiom of determinateness, PhD thesis, University of California, Berkeley (1977) . Google Scholar
R. A. Van Wesep , Cabal Seminar 76-77 , Lecture Notes in Mathematics 689 , eds. A. S. Kechris and Y. N. Moschovakis ( Springer-Verlag , 1978 ) . Google Scholar
W. W. Wadge. Reducibility and determinateness on the Baire space, PhD thesis, University of California, Berkeley (1983) . Google Scholar