Baire reflection
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- by Stevo Todorcevic and Stuart Zoble PDF
- Trans. Amer. Math. Soc. 360 (2008), 6181-6195 Request permission
Abstract:
We study reflection principles involving nonmeager sets and the Baire Property which are consequences of the generic supercompactness of $\omega _2$, such as the principle asserting that any point countable Baire space has a stationary set of closed subspaces of weight $\omega _1$ which are also Baire spaces. These principles entail the analogous principles of stationary reflection but are incompatible with forcing axioms. Assuming $MM$, there is a Baire metric space in which a club of closed subspaces of weight $\omega _1$ are meager in themselves. Unlike stronger forms of Game Reflection, these reflection principles do not decide $CH$, though they do give $\omega _2$ as an upper bound for the size of the continuum.References
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Additional Information
- Stevo Todorcevic
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4 – and – Universite Paris 7-CNRS, UMR 7056, 2 Place Jussieu, 75251 Paris Cedex 05, France
- MR Author ID: 172980
- Email: stevo@math.toronto.edu
- Stuart Zoble
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4
- Address at time of publication: Department of Mathematics, Wesleyan University, 265 Church Street, Middletown, Connecticut 06459-0128
- Email: azoble@wesleyan.edu
- Received by editor(s): March 10, 2006
- Published electronically: July 24, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 6181-6195
- MSC (2000): Primary 03E55; Secondary 03E50
- DOI: https://doi.org/10.1090/S0002-9947-08-04503-0
- MathSciNet review: 2434283