A note on $_ 2\textrm {sc}(\textbf {E}_ 1)$
HTML articles powered by AMS MathViewer
- by Rana Barua PDF
- Proc. Amer. Math. Soc. 103 (1988), 921-925 Request permission
Abstract:
We exhibit a set of reals recursive in ${{\mathbf {E}}_1}$ which is not in $\mathcal {C}$, the smallest $\sigma$-field containing analytic sets and closed under operation $\mathcal {A}$. As a consequence, a conjecture of Hinman is shown to be false.References
-
R. Barua, Studies in set-theoretic hierarchies: from Borel sets to $R$-sets, Ph.D. dissertation, Indian Statistical Institute, Calcutta, 1987.
- John P. Burgess, Classical hierarchies from a modern standpoint. I. $C$-sets, Fund. Math. 115 (1983), no.Β 2, 81β95. MR 699874, DOI 10.4064/fm-115-2-81-95
- John P. Burgess, Classical hierarchies from a modern standpoint. I. $C$-sets, Fund. Math. 115 (1983), no.Β 2, 81β95. MR 699874, DOI 10.4064/fm-115-2-81-95 P. G. Hinman, Ad astra per aspera: hierarchy schemata in recursive function theory, Ph.D. dissertation, Univ. of California, Berkeley, 1966.
- Peter G. Hinman, Hierarchies of effective descriptive set theory, Trans. Amer. Math. Soc. 142 (1969), 111β140. MR 265161, DOI 10.1090/S0002-9947-1969-0265161-3
- Peter G. Hinman, Recursion-theoretic hierarchies, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-New York, 1978. MR 499205, DOI 10.1007/978-3-662-12898-5
- Yiannis N. Moschovakis, Hyperanalytic predicates, Trans. Amer. Math. Soc. 129 (1967), 249β282. MR 236010, DOI 10.1090/S0002-9947-1967-0236010-2
- 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
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 921-925
- MSC: Primary 03D65; Secondary 03D55
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947683-X
- MathSciNet review: 947683