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On the equivalence of certain consequences of the proper forcing axiom

Published online by Cambridge University Press:  12 March 2014

Peter Nyikos  and
Leszek Piątkiewicz
Peter Nyikos
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, E-mail: [email protected]
Leszek Piątkiewicz
Affiliation:
Department of Mathematics, and Computer Science, Pembroke State University, Pembroke, NC 28372, E-mail: [email protected]
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Abstract

We prove that a number of axioms, each a consequence of PFA (the Proper Forcing Axiom) are equivalent. In particular we show that TOP (the Thinning-out Principle as introduced by Baumgartner in the Handbook of set-theoretic topology), is equivalent to the following statement: If I is an ideal on ω1 with ω1 generators, then there exists an uncountable X ⊆ ω1, such that either [X]ω ∩ I = ∅ or [X]ω ⊆ I.

Keywords

Proper Forcing AxiomTOP
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 431 - 443
Copyright
Copyright © Association for Symbolic Logic 1995

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References

REFERENCES

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