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Burke, Maxim R.
1998.
Set Theory.
p.
1.
Published online by Cambridge University Press: 12 March 2014
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.