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PROPER FORCING,CARDINAL ARITHMETIC,AND UNCOUNTABLE LINEAR ORDERS
PROPER FORCING CARDINAL ARITHMETIC UNCOUNTABLE LINEAR ORDERS
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2015/8/17
In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ1-definable in (H(ω2), ...
THE PROPER FORCING AXIOM,PRIKRY FORCING,AND THE SINGULAR CARDINALS HYPOTHESIS
FORCING AXIOM PRIKRY FORCING SINGULAR CARDINALS
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2015/8/17
The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous refl...
The Proper Forcing Axiom
Forcing axiom Martin’s Axiom OCA Open Coloring Axiom PID P-ideal Dichotomy proper forcing PFA
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2015/8/17
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 Co...
On the consistency strength of the proper forcing axiom
consistency strength proper forcing axiom
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2011/1/20
Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcin...