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CH with no Ostaszewski spaces

Author(s): Todd Eisworth; Judith Roitman
Journal: Trans. Amer. Math. Soc. 351 (1999), 2675-2693.
MSC (1991): Primary 03E35, 03E50, 54A35
Posted: March 8, 1999
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Abstract: There are models of CH without Ostaszeswki spaces. If $X$ is locally compact and sub-Ostaszewski, there is a forcing $P_X$ which does not add reals and which forces ``$X$ is not sub-Ostaszewski''.

References:

1.
U. Abraham and S. Todorcevic, Partition properties of $\omega _1$ compatible with CH, Fund. Math. 152 (1997), no. 2, 165-181. MR 98b:03064

2.
Alan Dow, More set theory for topologists, Top. and Appl. 64 (1995), 243-300. MR 97a:54005

3.
M. Goldstern, Tools for your forcing construction, Set Theory of the Reals (H. Judah, ed.), Bar-Ilan, 1993, pp. 305-360. MR 94h:03102

4.
A. Ostaszewski, On countably compact, perfectly normal spaces, J. London Math. Soc. 14 (1976), 505-516. MR 55:11210

5.
Saharon Shelah, Proper forcing, Springer-Verlag, New York, 1982. MR 84h:03002

6.
-, Proper and improper forcing, Perspectives in Mathematical Logic, Springer, Berlin, 1998. MR 98m:03002

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Additional Information:

Todd Eisworth
Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem, Israel
Address at time of publication: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: eisworth@math.huji.ac.il

Judith Roitman
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-0001
Email: roitman@math.ukans.edu

DOI: 10.1090/S0002-9947-99-02407-1
PII: S 0002-9947(99)02407-1
Keywords: Ostaszewski space, Continuum Hypothesis, iterated forcing
Received by editor(s): December 20, 1996
Received by editor(s) in revised form: November 23, 1997
Posted: March 8, 1999
Additional Notes: Research was done while the first author was a temporary assistant professor at the University of Kansas
Copyright of article: Copyright 1999, American Mathematical Society

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