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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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