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Cardinal invariants and the collapse of the continuum by Sacks forcing

  • Miroslav Repický (a1) (a2)

Abstract

We study cardinal invariants of systems of meager hereditary families of subsets of ω connected with the collapse of the continuum by Sacks forcing and we obtain a cardinal invariant such that collapses the continuum to and . Applying the Baumgartner-Dordal theorem on preservation of eventually narrow sequences we obtain the consistency of . We define two relations and on the set (ωω)Fin of finite-to-one functions which are Tukey equivalent to the eventual dominance relation of functions such that if -unbounded, well-ordered by , and not -dominating, then there is a nonmeager p-ideal. The existence of such a system follows from Martin's axiom. This is an analogue of the results of [3], [9, 10] for increasing functions.

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Cardinal invariants and the collapse of the continuum by Sacks forcing

  • Miroslav Repický (a1) (a2)

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