Dense non-reflection for stationary collections of countable 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

Dense non-reflection for stationary collections of countable sets

Authors:	David Asper , John Krueger,Yasuo Yoshinobu

Affiliation:	^aICREA and Universitat de Barcelona, Departament de Lògica, Universitat de Barcelona, C. Montalegre 6, Barcelona 08001, Spain;^bDepartment of Mathematics, University of California, Berkeley, CA, 94720, USA;^cGraduate School of Information Science, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8601, Japan

Abstract:	We present several forcing posets for adding a non-reflecting stationary subset of P_ω₁(λ), where λ≥ω₂. We prove that PFA is consistent with dense non-reflection in P_ω₁(λ), which means that every stationary subset of P_ω₁(λ) contains a stationary subset which does not reflect to any set of size ₁. If λ is singular with countable cofinality, then dense non-reflection in P_ω₁(λ) follows from the existence of squares.

Keywords:	Dense non-reflection Proper forcing axiom
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