Sacks forcing and the total failure of Martin's Axiom
نویسندگان
چکیده
منابع مشابه
Sacks forcing, Laver forcing, and Martin's axiom
In this paper we study the question assuming MA+¬CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalant to question of what is the additivity of Marczewski’s ideal s. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals. Introduction Let S be Sacks perfe...
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We answer a question of Jockusch by constructing a hyperimmunefree minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.
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We consider a property stronger than the Sacks property which holds between the ground model and the Sacks forcing extension. 1. The Shrink Wrapping Property Suppose that V is a Sacks forcing extension of a model M . Then the Sacks property holds between V and M . That is, for each x ∈ ω, there exists a tree T ⊆ ω in M such that x ∈ [T ] and each level of T is finite. The following is a stronge...
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The Proper Forcing Axiom is a powerful extension of the Baire Category Theorem which has proved highly effective in settling mathematical statements which are independent of ZFC. In contrast to the Continuum Hypothesis, it eliminates a large number of the pathological constructions which can be carried out using additional axioms of set theory. Mathematics Subject Classification (2000). Primary...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1985
ISSN: 0166-8641
DOI: 10.1016/0166-8641(85)90002-1