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Proceedings of the American Mathematical Society

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Evading predictors with creatures

Author: Otmar Spinas
Journal: Proc. Amer. Math. Soc. 126 (1998), 2103-2115
MSC (1991): Primary 03E05, 03E35
MathSciNet review: 1452829
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Abstract: We continue the theory of evasion and prediction which was introduced by Blass and developed by Brendle, Shelah, and Laflamme. We prove that for arbitrary sufficiently different $f,g\in\ ^{\omega }\!\omega $, it is consistent to have ${\mathfrak{e}}_{g}<{\mathfrak{e}}_{f}$, where ${\mathfrak{e}}_{f}$ is the evasion number of the space $\prod _{n<\o }f(n)$. For this we apply a variant of Shelah's ``creature forcing''.

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  • [B] A. Blass, Cardinal characteristics and the product of countably many infinite cyclic groups, Journal of Algebra, vol.169 (1994), pp.512-540. MR 95h:20069
  • [Br] J. Brendle, Evasion and prediction - the Specker phenomenon and Gross spaces, Forum Mathematicum, vol.7 (1995), pp.513-541. MR 96i:03042
  • [BrSh] J. Brendle and S. Shelah, Evasion and prediction II, Journal of the London Mathematical Society, vol.53, (1996), pp.19-27. MR 97d:03061
  • [GSh] M. Goldstern and S. Shelah, Many simple cardinal invariants, Archive for Mathematical Logic, vol.32 (1993), pp.203-221. MR 94c:03064
  • [L] C. Laflamme, Combinatorial aspects of $F_{\sigma }$ filters with an application to ${\mathcal{N}}$-sets, Proc. AMS, to appear. CMP 96:16
  • [RSh1] A. Roslanowski and S. Shelah, Localizations of infinite subsets of $\omega $, Arch. Math. Logic 35 (1996), 315-339. CMP 97:04
  • [RSh2] A. Roslanowski and S. Shelah, Norms on possibilities I, preprint, pp.1-186, (publication 470 in Shelah's list of publications).
  • [Sh1] S. Shelah, On cardinal invariants of the continuum, in: Contemporary Mathematics, vol.31 (1984), pp.183-207. MR 86b:03064
  • [Sh2] S. Shelah, Vive la difference I: Nonisomorphism of ultrapowers of countable models, in: Set theory of the continuum, MSRI publications, vol.26 (1992), pp.357-405. MR 94g:03068
  • [Sh3] S. Shelah, Proper forcing, Lecture Notes in Math., vol. 940, Springer-Verlag (1982). MR 84h:03002
  • [ShSp1] S. Shelah and O. Spinas, Gross spaces, Trans. AMS, vol.348 (1996), pp.4257-4277. MR 96m:03031
  • [ShSp2] S. Shelah and O. Spinas, The distributivity numbers of ${\mathcal{P}}(\omega )/fin$ and its square, Trans. AMS, to appear.
  • [Sp] O. Spinas, Cardinal invariants and quadratic forms, in: Israel Mathematical Conference Proceedings, vol.6 (1993), pp.563-581. MR 94f:03059

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Additional Information

Otmar Spinas
Affiliation: Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
Address at time of publication: Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany

Additional Notes: Partially supported by a research fellowship of the Alexander von Humboldt Foundation.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1998 American Mathematical Society