Evading predictors with creatures

Author:
Otmar Spinas

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2103-2115

MSC (1991):
Primary 03E05, 03E35

DOI:
https://doi.org/10.1090/S0002-9939-98-04410-4

MathSciNet review:
1452829

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 , it is consistent to have , where is the evasion number of the space . For this we apply a variant of Shelah's ``creature forcing''.

**[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 filters with an application to -sets,*Proc. AMS, to appear. CMP**96:16****[RSh1]**A. Roslanowski and S. Shelah,*Localizations of infinite subsets of ,*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 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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
03E05,
03E35

Retrieve articles in all journals with MSC (1991): 03E05, 03E35

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

Email:
spinas@math.ethz.ch

DOI:
https://doi.org/10.1090/S0002-9939-98-04410-4

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