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Hyperarithmetically encodable sets. (English) Zbl 0411.03039


MSC:

03D60 Computability and recursion theory on ordinals, admissible sets, etc.
03E15 Descriptive set theory
03D30 Other degrees and reducibilities in computability and recursion theory

Citations:

Zbl 0402.03040
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Full Text: DOI

References:

[1] Stȧl Aanderaa, Inductive definitions and their closure ordinals, Generalized recursion theory (Proc. Sympos., Univ. Oslo, Oslo, 1972), North-Holland, Amsterdam, 1974, pp. 207 – 220. Studies in Logic and the Foundations of Math., Vol. 79.
[2] P. Aczel, Representability in some systems of second order arithmetic, Israel J. Math. 8 (1970), 309 – 328. · Zbl 0216.00602 · doi:10.1007/BF02798678
[3] Peter Aczel and Wayne Richter, Inductive definitions and analogues of large cardinals, Conference in Mathematical Logic — London ’70 (Proc. Conf., Bedford Coll., London, 1970) Springer, Berlin, 1972, pp. 1 – 9. Lecture Notes in Math., Vol. 255. · Zbl 0272.02065
[4] Fred Galvin and Karel Prikry, Borel sets and Ramsey’s theorem, J. Symbolic Logic 38 (1973), 193 – 198. · Zbl 0276.04003 · doi:10.2307/2272055
[5] R. Björn Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229 – 308; erratum, ibid. 4 (1972), 443. With a section by Jack Silver. · Zbl 0257.02035 · doi:10.1016/0003-4843(72)90001-0
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[7] Carl G. Jockusch Jr. and Robert I. Soare, Encodability of Kleene’s \?, J. Symbolic Logic 38 (1973), 437 – 440. · Zbl 0279.02025 · doi:10.2307/2273040
[8] Alexander S. Kechris, The theory of countable analytical sets, Trans. Amer. Math. Soc. 202 (1975), 259 – 297. · Zbl 0317.02082
[9] Azriel Lévy, Definability in axiomatic set theory. I, Logic, Methodology and Philos. Sci. (Proc. 1964 Internat. Congr.), North-Holland, Amsterdam, 1965, pp. 127 – 151.
[10] A. R. D. Mathias, On a generalization of Ramsey’s theorem, Notices Amer. Math. Soc. 15 (1968), 931. Abstract #68T-E19; Lecture Notes in Math., Springer-Verlag, Berlin (to appear).
[11] Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967.
[12] G. E. Sacks and S. G. Simpson, The \?-finite injury method, Ann. Math. Logic 4 (1972), 343 – 367. · Zbl 0262.02037 · doi:10.1016/0003-4843(72)90004-6
[13] J. R. Shoenfield, Unramified forcing, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 357 – 381.
[14] Robert I. Soare, Sets with no subset of higher degree, J. Symbolic Logic 34 (1969), 53 – 56. · Zbl 0182.01602 · doi:10.2307/2270981
[15] Robert M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1 – 56. · Zbl 0207.00905 · doi:10.2307/1970696
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