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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Borel games and the Baire property
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by Kenneth Schilling and Robert Vaught PDF
Trans. Amer. Math. Soc. 279 (1983), 411-428 Request permission

Abstract:

The Borel game operations are a natural generalization of the operation $(\text {A})$. It is shown that these operations preserve the property of Baire in all topological spaces. Applications are given to invariant descriptive set theory and the model theory of infinitary logic.
References
    J. Burgess, Infinitary languages and descriptive set theory, Ph.D. thesis, Univ. of California, Berkeley, Calif., 1974.
  • Jens Erik Fenstad and Dag Normann, On absolutely measurable sets, Fund. Math. 81 (1973/74), no. 2, 91–98. MR 338299, DOI 10.4064/fm-81-2-91-98
  • David Gale and F. M. Stewart, Infinite games with perfect information, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N.J., 1953, pp. 245–266. MR 0054922
  • Alexander S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337–384. MR 369072, DOI 10.1016/0003-4843(73)90012-0
  • Alexander S. Kechris, Forcing in analysis, Higher set theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977) Lecture Notes in Math., vol. 669, Springer, Berlin, 1978, pp. 277–302. MR 520191
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • Donald A. Martin, Borel determinacy, Ann. of Math. (2) 102 (1975), no. 2, 363–371. MR 403976, DOI 10.2307/1971035
  • D. Miller, Invariant descriptive set theory and the topological approach to model theory, Ph.D. thesis, Univ. of California, Berkeley, Calif., 1976.
  • John C. Oxtoby, The Banach-Mazur game and Banach category theorem, Contributions to the theory of games, vol. 3, Annals of Mathematics Studies, no. 39, Princeton University Press, Princeton, N.J., 1957, pp. 159–163. MR 0093741
  • G. Reyes, Typical and generic relations in a Baire space for models, Ph.D. thesis, Univ. of California, Berkeley, Calif., 1967. K. Schilling, Absolutely ${\mathbf {\Delta } ^1}_2$ operations and the Baire property, Abstracts Amer. Math. Soc. 1 (1980), 239. Abstract #80T-E22.
  • Roman Sikorski, Boolean algebras, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 25, Springer-Verlag New York, Inc., New York, 1969. MR 0242724
  • Robert Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974/75), 269–294. MR 363912, DOI 10.4064/fm-82-3-269-294
  • R. Vaught and K. Schilling, Borel game operations and the Baire property, Notices Amer. Math. Soc. 26 (1979), A-247. Abstract #764-E1.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 279 (1983), 411-428
  • MSC: Primary 04A15; Secondary 03C15, 54H05
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0704624-8
  • MathSciNet review: 704624