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Complexity of winning strategies for $ \Delta\sp 0\sb 2$ games


Author: Rana Barua
Journal: Proc. Amer. Math. Soc. 117 (1993), 227-233
MSC: Primary 03D65
DOI: https://doi.org/10.1090/S0002-9939-1993-1119261-5
MathSciNet review: 1119261
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Abstract: For a $ \Delta _2^0$ game played on $ \omega $, we show that the winning player has a winning strategy that is recursive in $ {\mathbb{E}_1}$, where $ {\mathbb{E}_1}$ is the total type-$ 2$ object that embodies operation $ \mathcal{A}$.


References [Enhancements On Off] (What's this?)

  • [1] P. Aczel, Representations of some systems of second order arithmetic, Israel J. Math. 8 (1970), 309-328. MR 0269501 (42:4396)
  • [2] R. Barua, Structure of hyperarithmetical sets of ambiguous Borel classes, I. S. I. Tech. Report no. 15/85, 1985.
  • [3] -, A note on $ _2\operatorname{sc} ({\mathbb{E}_1})$, Proc. Amer. Math. Soc. 103 (1988), 921-925. MR 947683 (89h:03079)
  • [4] J. P. Burgess, Classical hierarchies from a modern standpoint, Part I: $ \mathcal{C}$-sets, Fund. Math. 115 (1983), 81-95; Part II: $ R$-sets, 97-105.
  • [5] P. G. Hinman, Recursion theoretic hierarchies, Springer-Verlag, Berlin, Heidelberg, and New York, 1978. MR 499205 (82b:03084)
  • [6] -, Hierarchies of effective descriptive set theory, Trans. Amer. Math. Soc. 142 (1969), 111-140. MR 0265161 (42:74)
  • [7] T. John, Recursion in Kolmogorov's $ \mathbb{R}$-operator and the ordinal $ {\sigma _3}$, J. Symbolic Logic 51 (1986), 1-11. MR 830066 (87i:03094)
  • [8] K. Kuratowski, Topology, Vol. I, Academic Press, New York and London, 1966. MR 0217751 (36:840)
  • [9] A. Louveau, A separation theorem for $ \Sigma _1^1$ sets, Trans. Amer. Math. Soc. 260 (1980), 363-378. MR 574785 (81j:04001)
  • [10] Y. N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, New York, and Oxford, 1980. MR 561709 (82e:03002)

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DOI: https://doi.org/10.1090/S0002-9939-1993-1119261-5
Article copyright: © Copyright 1993 American Mathematical Society

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