Authors: Todorčević, Stevo 
Zoble, Stuart
Title: Baire reflection
Journal: Transactions of the American Mathematical Society
Volume: 360
Issue: 12
First page: 6181
Last page: 6195
Issue Date: 1-Dec-2008
Rank: M21
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-08-04503-0
We study reflection principles involving nonmeager sets and the Baire Property which are consequences of the generic supercompactness of ω2, such as the principle asserting that any point countable Baire space has a stationary set of closed subspaces of weight ω1 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 ω1 are meager in themselves. Unlike stronger forms of Game Reflection, these reflection principles do not decide CH, though they do give ω2 as an upper bound for the size of the continuum.
Keywords: Baire Property | Game Reflection | Martin's Maximum
Publisher: American Mathematical Society

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