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Cardinal invariants and the collapse of the continuum by Sacks forcing

Published online by Cambridge University Press:  12 March 2014

Miroslav Repický
Miroslav Repický*
Affiliation:
Mathematical Institute, Slovak Academy of Sciences, Jesenná 5. 041 54 Košice., Slovak Republic Institute of Computer Science, Faculty of Science, P. J. Šafárik University, Jesenná 5. 041 54 Košice., Slovak Republic, E-mail: repicky@kosice.upjs.sk, URL: kosice.upjs.sk/~repicky
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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.

Keywords

Sacks forcingcardinal invariantshereditary familieseventually narrow sequencesfinite-to-one functions
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 2 , June 2008 , pp. 711 - 728
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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