Forcing indestructibility of set-theoretic axioms
نویسنده
چکیده
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to א1. Later we give applications, among them the consistency of MM with אω not being Jonsson which answers a question raised during Oberwolfach 2005.
منابع مشابه
Forcing indestructibility of MAD families
Let A ⊆ [ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families wh...
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ورودعنوان ژورنال:
- J. Symb. Log.
دوره 72 شماره
صفحات -
تاریخ انتشار 2007