Journal of Symbolic Logic

Cardinal invariants of monotone and porous sets

Michael Hrušák and Ondřej Zindulka

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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.

Article information

J. Symbolic Logic, Volume 77, Issue 1 (2012), 159-173.

First available in Project Euclid: 20 January 2012

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Zentralblatt MATH identifier

Primary: 28A75,03E15,03E17,03E35,54H05

σ-monotone σ-porous cardinal invariants


Hrušák, Michael; Zindulka, Ondřej. Cardinal invariants of monotone and porous sets. J. Symbolic Logic 77 (2012), no. 1, 159--173. doi:10.2178/jsl/1327068697.

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