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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the Weak Reflection Principle


Author: John Krueger
Journal: Trans. Amer. Math. Soc. 363 (2011), 5537-5576
MSC (2010): Primary 03E35; Secondary 03E05
Published electronically: May 13, 2011
MathSciNet review: 2813424
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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)$.


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Additional Information

John Krueger
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203
Email: jkrueger@unt.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05310-9
PII: S 0002-9947(2011)05310-9
Keywords: Weak Reflection Principle, Reflection Principle, generalized stationarity
Received by editor(s): May 30, 2009
Received by editor(s) in revised form: February 8, 2010
Published electronically: May 13, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.