On a fragment of the universal Baire property for  <IMG WIDTH="29" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="/proc/2008-136-05/S0002-9939-08-08918-1/gif-title0/img1.gif" ALT="$ \Sigma^1_2$"> sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On a fragment of the universal Baire property for $\Sigma^1_2$ sets

Authors:	Stuart Zoble

Institution:	Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4

Abstract:	There is a well-known global equivalence between $\Sigma^1_2$ sets having the universal Baire property, two-step $\Sigma^1_3$ generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of $\Sigma^1_2$ sets being $(2^{\omega})^{+}$ -cc-universally Baire, which is below $0^{\char93 }$ . In a model obtained, there is a $\Sigma^1_2$ set which is weakly $\omega_2$ -universally Baire but not $\omega_2$ -universally Baire.

Keywords:	Generic absoluteness universal Baire property

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