×

zbMATH — the first resource for mathematics

On a notion of smallness for subsets of the Baire space. (English) Zbl 0401.03022

MSC:
03E15 Descriptive set theory
03E60 Determinacy principles
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. R. Busch, Some problems connected with the axiom of determinacy, Ph. D. Thesis, Rockefeller Univ., 1972.
[2] Morton Davis, Infinite games of perfect information, Advances in game theory, Princeton Univ. Press, Princeton, N.J., 1964, pp. 85 – 101. · Zbl 0133.13104
[3] Jens Erik Fenstad, The axiom of determinateness, Proceedings of the Second Scandinavian Logic Symposium (Univ. Oslo, Oslo, 1970) North-Holland, Amsterdam, 1971, pp. 41 – 61. Studies in Logic and the Foundations of Mathematics, Vol. 63. · Zbl 0222.02076
[4] Harvey M. Friedman, Borel sets and hyperdegrees, J. Symbolic Logic 38 (1973), 405 – 409. · Zbl 0335.02028 · doi:10.2307/2273034 · doi.org
[5] -, A basis theorem for L (circulated notes).
[6] D. Guaspari, Thin and wellordered analytical sets, Ph.D. Thesis, Univ. of Cambridge, 1972.
[7] Stephen H. Hechler, On the existence of certain cofinal subsets of ^\?\?, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1974, pp. 155 – 173.
[8] A. S. Kechris, Lecture notes on descriptive set theory, M.I.T., Cambridge, Mass., 1973.
[9] Alexander S. Kechris, The theory of countable analytical sets, Trans. Amer. Math. Soc. 202 (1975), 259 – 297. · Zbl 0317.02082
[10] Alexander S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337 – 384. · Zbl 0277.02019 · doi:10.1016/0003-4843(73)90012-0 · doi.org
[11] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. · Zbl 0158.40901
[12] D. A. Martin, \( \Delta _{2n}^1\) determinacy implies \( \Sigma _{2n}^1\) determinacy, 1973 (circulated notes).
[13] -, Countable \( \Sigma _{2n + 1}^1\) sets, 1972 (circulated notes).
[14] Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. · Zbl 0433.03025
[15] Yiannis N. Moschovakis, Determinacy and prewellorderings of the continuum, Mathematical Logic and Foundations of Set Theory (Proc. Internat. Colloq., Jerusalem, 1968) North-Holland, Amsterdam, 1970, pp. 24 – 62.
[16] Y. N. Moschovakis, Analytical definability in a playful universe, Logic, methodology and philosophy of science, IV (Proc. Fourth Internat. Congr., Bucharest, 1971) North-Holland, Amsterdam, 1973, pp. 77 – 85. Studies in Logic and Foundations of Math., Vol. 74.
[17] Yiannis N. Moschovakis, Uniformization in a playful universe, Bull. Amer. Math. Soc. 77 (1971), 731 – 736. · Zbl 0232.04002
[18] Jan Mycielski, On the axiom of determinateness, Fund. Math. 53 (1963/1964), 205 – 224. · Zbl 0168.25101
[19] Jan Mycielski and S. Świerczkowski, On the Lebesgue measurability and the axiom of determinateness, Fund. Math. 54 (1964), 67 – 71. · Zbl 0147.19503
[20] John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. · Zbl 0435.28011
[21] Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967.
[22] Joseph R. Shoenfield, Mathematical logic, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967. · Zbl 0155.01102
[23] Jacques Stern, Some measure theoretic results in effective descriptive set theory, Israel J. Math. 20 (1975), no. 2, 97 – 110. · Zbl 0322.02061 · doi:10.1007/BF02757880 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.