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...
متن کاملMartin's axiom and D21 well-ordering of the reals
Assuming an inaccessible cardinal κ, there is a generic extension in which MA+ 20 = κ holds and the reals have a ∆1 well-ordering.
متن کاملBounded Proper Forcing Axiom and Well Orderings of the Reals
We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω1) which is ∆1 definable with parameter a subset of ω1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes א2 and also satisfies BPFA must contain all subsets of ω1. We show as applications how to build minimal models of BPFA and that BPFA implies t...
متن کاملThe Bounded Proper Forcing Axiom and Well Orderings of the Reals
We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω1) which is Δ1 definable with parameter a subset of ω1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes א2 and also satisfies BPFA must contain all subsets of ω1. We show as applications how to build minimal models of BPFA and that BPFA implies t...
متن کاملTHE URYSOHN AXIOM AND THE COMPLETELY HAUSDORFF AXIOM IN L-TOPOLOGICAL SPACES
In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1989
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-133-2-161-168