On the Weak Reflection Principle
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- by John Krueger PDF
- Trans. Amer. Math. Soc. 363 (2011), 5537-5576 Request permission
Abstract:
The Weak Reflection Principle for $\omega _2$, or $\textrm {WRP}(\omega _2)$, is the statement that every stationary subset of $P_{ \omega _1}(\omega _2)$ reflects to an uncountable ordinal in $\omega _2$. The Reflection Principle for $\omega _2$, or $\textrm {RP}(\omega _2)$, is the statement that every stationary subset of $P_{ \omega _1 } ( \omega _2 )$ reflects to an ordinal in $\omega _2$ with cofinality $\omega _1$. Let $\kappa$ be a $\kappa ^+$-supercompact cardinal and assume $2^{\kappa } = \kappa ^+$. Then there exists a forcing poset $\mathbb {P}$ which collapses $\kappa$ to become $\omega _2$, and $\Vdash _{\mathbb {P}} \textrm {WRP}(\omega _2) \land \neg \textrm {RP}(\omega _2)$.References
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Additional Information
- John Krueger
- Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203
- MR Author ID: 720328
- Email: jkrueger@unt.edu
- Received by editor(s): May 30, 2009
- Received by editor(s) in revised form: February 8, 2010
- Published electronically: May 13, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 5537-5576
- MSC (2010): Primary 03E35; Secondary 03E05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05310-9
- MathSciNet review: 2813424