Thin stationary sets and disjoint club sequences
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- by Sy-David Friedman and John Krueger PDF
- Trans. Amer. Math. Soc. 359 (2007), 2407-2420 Request permission
Abstract:
We describe two opposing combinatorial properties related to add- ing clubs to $\omega _2$: the existence of a thin stationary subset of $P_{\omega _1}(\omega _2)$ and the existence of a disjoint club sequence on $\omega _2$. A special Aronszajn tree on $\omega _2$ implies there exists a thin stationary set. If there exists a disjoint club sequence, then there is no thin stationary set, and moreover there is a fat stationary subset of $\omega _2$ which cannot acquire a club subset by any forcing poset which preserves $\omega _1$ and $\omega _2$. We prove that the existence of a disjoint club sequence follows from Martin’s Maximum and is equiconsistent with a Mahlo cardinal.References
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Additional Information
- Sy-David Friedman
- Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Waehringer Strasse 25, A-1090 Wien, Austria
- MR Author ID: 191285
- Email: sdf@logic.univie.ac.at
- John Krueger
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 720328
- Email: jkrueger@math.berkeley.edu
- Received by editor(s): June 28, 2005
- Published electronically: December 5, 2006
- Additional Notes: The authors were supported by FWF project number P16790-N04.
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 2407-2420
- MSC (2000): Primary 03E35, 03E40
- DOI: https://doi.org/10.1090/S0002-9947-06-04163-8
- MathSciNet review: 2276627