On the Equivalence of Certain Consequences of the Proper Forcing Axiom
Nyikos, Peter ; Piatkiewicz, Leszek
J. Symbolic Logic, Tome 60 (1995) no. 1, p. 431-443 / Harvested from Project Euclid
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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 $\omega_1$ with $\omega_1$ generators, then there exists an uncountable $X \subseteq \omega_1$, such that either $\lbrack X\rbrack^\omega \cap I = \oslash$ or $\lbrack X\rbrack^\omega \subseteq I$.
Publié le : 1995-06-14
Classification:  Proper Forcing Axiom,  TOP,  03E65 
@article{1183744745,
     author = {Nyikos, Peter and Piatkiewicz, Leszek},
     title = {On the Equivalence of Certain Consequences of the Proper Forcing Axiom},
     journal = {J. Symbolic Logic},
     volume = {60},
     number = {1},
     year = {1995},
     pages = { 431-443},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744745}
}

Nyikos, Peter; Piatkiewicz, Leszek. On the Equivalence of Certain Consequences of the Proper Forcing Axiom. J. Symbolic Logic, Tome 60 (1995) no. 1, pp.  431-443. http://gdmltest.u-ga.fr/item/1183744745/