Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Borel games and the Baire property


Authors: Kenneth Schilling and Robert Vaught
Journal: Trans. Amer. Math. Soc. 279 (1983), 411-428
MSC: Primary 04A15; Secondary 03C15, 54H05
MathSciNet review: 704624
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Borel game operations are a natural generalization of the operation $ ($A$ )$. 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 [Enhancements On Off] (What's this?)

  • [1] J. Burgess, Infinitary languages and descriptive set theory, Ph.D. thesis, Univ. of California, Berkeley, Calif., 1974.
  • [2] Jens Erik Fenstad and Dag Normann, On absolutely measurable sets, Fund. Math. 81 (1973/74), no. 2, 91–98. Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday, II. MR 0338299 (49 #3065)
  • [3] 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 (14,999b)
  • [4] Alexander S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337–384. MR 0369072 (51 #5308)
  • [5] 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 (80c:03051)
  • [6] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York, 1966. MR 0217751 (36 #840)
  • [7] Donald A. Martin, Borel determinacy, Ann. of Math. (2) 102 (1975), no. 2, 363–371. MR 0403976 (53 #7785)
  • [8] D. Miller, Invariant descriptive set theory and the topological approach to model theory, Ph.D. thesis, Univ. of California, Berkeley, Calif., 1976.
  • [9] 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 (20 #264)
  • [10] G. Reyes, Typical and generic relations in a Baire space for models, Ph.D. thesis, Univ. of California, Berkeley, Calif., 1967.
  • [11] K. Schilling, Absolutely $ {\mathbf{\Delta} ^1}_2$ operations and the Baire property, Abstracts Amer. Math. Soc. 1 (1980), 239. Abstract #80T-E22.
  • [12] Roman Sikorski, Boolean algebras, Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 25, Springer-Verlag New York Inc., New York, 1969. MR 0242724 (39 #4053)
  • [13] Robert Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974/75), 269–294. Collection of articles dedicated to Andrzej Mostowski on his sixtieth birthday, VII. MR 0363912 (51 #167)
  • [14] R. Vaught and K. Schilling, Borel game operations and the Baire property, Notices Amer. Math. Soc. 26 (1979), A-247. Abstract #764-E1.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 04A15, 03C15, 54H05

Retrieve articles in all journals with MSC: 04A15, 03C15, 54H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0704624-8
PII: S 0002-9947(1983)0704624-8
Article copyright: © Copyright 1983 American Mathematical Society