Kechris, Alexander S. (1978) On Transfinite Sequences of Projective Sets with an Application to ∑^1_2 Equivalence Relations. In: Logic Colloquium '77. Studies in Logic and the Foundations of Mathematics. No.96. North Holland Publishing Company , Amsterdam, pp. 155-160. ISBN 9780444851789. https://resolver.caltech.edu/CaltechAUTHORS:20130530-070413635
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Abstract
This chapter focuses on transfinite sequences of projective sets with an application to Σ^1_(∼2n) equivalence relations. From the full axiom of determinacy (AD), the chapter demonstrates that the class of Σ^1_(∼2n) sets is closed under well ordered unions. This result is then applied to compute the maximum length of transfinite 1–1 sequences of ^1_(∼2n) sets, from AD again. As a further application, the chapter demonstrates that in the real world, every Σ^1_2 equivalence relation has either ≤_א1k, or 2_0^א equivalence classes. In addition, the cardinality of the maximum length of a transfinite sequence of ^1_(∼2n) sets without repetitions is computed in the chapter.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 1978 North-Holland Publishing Company. Published by Elsevier B.V. Research and preparation for this paper were partially supported by NSF Grants MPS75-07562 and MCS76-17254. | |||||||||
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| Series Name: | Studies in Logic and the Foundations of Mathematics | |||||||||
| Issue or Number: | 96 | |||||||||
| DOI: | 10.1016/S0049-237X(08)71998-0 | |||||||||
| Record Number: | CaltechAUTHORS:20130530-070413635 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130530-070413635 | |||||||||
| Official Citation: | Alexander S. Kechris, On Transfinite Sequences of Projective Sets with an Application to ∑12 Equivalence Relations, In: Angus Macintyre, Leszek Pacholski and Jeff Paris, Editor(s), Studies in Logic and the Foundations of Mathematics, Elsevier, 1978, Volume 96, Pages 155-160, ISSN 0049-237X, ISBN 9780444851789, 10.1016/S0049-237X(08)71998-0. (http://www.sciencedirect.com/science/article/pii/S0049237X08719980) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 38708 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 30 May 2013 17:15 | |||||||||
| Last Modified: | 09 Nov 2021 23:39 |
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