The bounded proper forcing axiom and well orderings of the reals

被引：0
|
作者：
Caicedo, Andres Eduardo
Velickovic, Boban
机构：
[1] CALTECH, Dept Math, Pasadena, CA 91125 USA
[2] Univ Paris 07, UFR Math, Equipe Log Math, F-75251 Paris 05, France
来源：
MATHEMATICAL RESEARCH LETTERS | 2006年 / 13卷 / 2-3期
关键词：
BPFA; MRP; definable well orderings; inner models; Hartig quantifier;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(omega(1)) which is Delta(1) definable with parameter a subset of omega(1). Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes N-2 and also satisfies BPFA must contain all subsets of omega(1). We show as applications how to build minimal models of BPFA and that BPFA implies that the decision problem for the Hartig quantifier is not lightface projective.
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页码：393 / 408
页数：16
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