Rich sets
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- by C. T. Chong
- Proc. Amer. Math. Soc. 80 (1980), 458-460
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581005-4
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Abstract:
Let ${(V = L)_\alpha }$ say that every bounded subset of $\alpha$ is an element of ${L_\alpha }$. We show that if ${(V = L)_\alpha }$, then every $X \subseteq \alpha$ of order-type $\alpha$ is rich, in the sense that every $\alpha$-degree above that of X is represented by a subset of X.References
- Carl G. Jockusch Jr., Upward closure and cohesive degrees, Israel J. Math. 15 (1973), 332–335. MR 347573, DOI 10.1007/BF02787575
- E. M. Kleinberg, Infinitary combinatorics, Cambridge Summer School in Mathematical Logic (Cambridge, 1971) Lecture Notes in Math., Vol. 337, Springer, Berlin, 1973, pp. 361–418. MR 0337631
- Stephen G. Simpson, Sets which do not have subsets of every higher degree, J. Symbolic Logic 43 (1978), no. 1, 135–138. MR 495125, DOI 10.2307/2271956
- Robert I. Soare, Sets with no subset of higher degree, J. Symbolic Logic 34 (1969), 53–56. MR 263627, DOI 10.2307/2270981 J. Stillwell, Reducibility in generalized recursion theory, Ph. D. thesis, M.I.T., 1970.
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 458-460
- MSC: Primary 03D60; Secondary 03D30
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581005-4
- MathSciNet review: 581005