Perfect sets and collapsing continuum
Repický, Miroslav
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003), p. 315-327 / Harvested from Czech Digital Mathematics Library
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Under Martin's axiom, collapsing of the continuum by Sacks forcing $\Bbb S$ is characterized by the additivity of Marczewski's ideal (see [4]). We show that the same characterization holds true if $\frak d=\frak c$ proving that under this hypothesis there are no small uncountable maximal antichains in $\Bbb S$. We also construct a partition of $^\omega 2$ into $\frak c$ perfect sets which is a maximal antichain in $\Bbb S$ and show that $s^0$-sets are exactly (subsets of) selectors of maximal antichains of perfect sets.

Publié le : 2003-01-01
Classification:  03E17,  03E40,  03E50,  54A35 
@article{119388,
     author = {Miroslav Repick\'y},
     title = {Perfect sets and collapsing continuum},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {44},
     year = {2003},
     pages = {315-327},
     zbl = {1104.03045},
     mrnumber = {2026166},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119388}
}

Repický, Miroslav. Perfect sets and collapsing continuum. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 315-327. http://gdmltest.u-ga.fr/item/119388/

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