A theorem about $\Sigma ^1_1$ equivalence relations
HTML articles powered by AMS MathViewer
- by Howard Becker PDF
- Proc. Amer. Math. Soc. 150 (2022), 2729-2731 Request permission
Abstract:
Any $\Sigma ^1_1$ equivalence relation which is invariant under hyperarithmetic equivalence is also invariant under admissible ordinal equivalence.References
- Howard Becker, Assigning an isomorphism type to a hyperdegree, J. Symb. Log. 85 (2020), no. 1, 325–337. MR 4089387, DOI 10.1017/jsl.2019.81
- Su Gao, Invariant descriptive set theory, Pure and Applied Mathematics (Boca Raton), vol. 293, CRC Press, Boca Raton, FL, 2009. MR 2455198
- Leo Harrington, Analytic determinacy and $0^{\sharp }$, J. Symbolic Logic 43 (1978), no. 4, 685–693. MR 518675, DOI 10.2307/2273508
- Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
- Antonio Montalbán, Degree-invariant, analytic equivalence relations without perfectly many classes, Proc. Amer. Math. Soc. 145 (2017), no. 1, 395–398. MR 3565390, DOI 10.1090/proc/13218
- Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
- Gerald E. Sacks, Countable admissible ordinals and hyperdegrees, Advances in Math. 20 (1976), no. 2, 213–262. MR 429523, DOI 10.1016/0001-8708(76)90187-0
- John R. Steel, Forcing with tagged trees, Ann. Math. Logic 15 (1978), no. 1, 55–74. MR 511943, DOI 10.1016/0003-4843(78)90026-8
Additional Information
- Howard Becker
- Affiliation: PMB 128, 4711 Forest Dr., Ste. 3, Columbia, South Carolina 29206
- MR Author ID: 33335
- Email: hsbecker@hotmail.com
- Received by editor(s): May 27, 2021
- Received by editor(s) in revised form: October 12, 2021
- Published electronically: March 7, 2022
- Communicated by: Vera Fischer
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2729-2731
- MSC (2020): Primary 03E15
- DOI: https://doi.org/10.1090/proc/15884
- MathSciNet review: 4399285