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March 2012 Cardinal invariants of monotone and porous sets
Michael Hrušák, Ondřej Zindulka
J. Symbolic Logic 77(1): 159-173 (March 2012). DOI: 10.2178/jsl/1327068697

Abstract

A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y)≤ c d(x,z) for all x<y<z in X. We investigate cardinal invariants of the σ-ideal Mon generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are also investigated. In particular, we show that non(Mon)≥𝔪σ-linked, but non(Mon)<𝔪σ-centered is consistent. Also cov(Mon)<𝔠 and cof(𝒩)<cov(Mon) are consistent.

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Michael Hrušák. Ondřej Zindulka. "Cardinal invariants of monotone and porous sets." J. Symbolic Logic 77 (1) 159 - 173, March 2012. https://doi.org/10.2178/jsl/1327068697

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1245.28003
MathSciNet: MR2951635
Digital Object Identifier: 10.2178/jsl/1327068697

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Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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