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Hechler's Theorem for tall analytic P-ideals

  • Barnabás Farkas (a1)

Abstract

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal (coded in the ground model) a cofinal subset of is order isomorphic to (Q, ≤).

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[1]Bartoszynski, Tomek and Kada, Masaru, Hechler's theorem for the meager ideal, Topology and its Applications, vol. 146–147 (2005), pp. 429435.
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[3]Burke, Maxim R. and Kada, Masaru, Hechler's theorem for the null ideal, Archive for Mathematical Logic, vol. 43 (2004), pp. 703722.
[4]Fremlin, David H., Measure theory. Set-theoretic measure theory, Torres Fremlin, Colchester, England, 2004, available at http://www.essex.ac.uk/maths/staff/fremlin/mt.html.
[5]Hechler, S. H., On the existence of certain cofinal subsets of ωω, Axiomatic set theory (Jech, Thomas, editor), American Mathematical Society, 1974, pp. 155173.
[6]Solecki, Slamowir, Analytic P-ideals and their applications, Annals of Pure and Applied Logic, vol. 99 (1999), pp. 5172.
[7]Soukup, Lajos, Pcf theory and cardinal invariants of the reals, unpublished notes, 2001.

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