Journal of Symbolic Logic

Cardinal invariants of monotone and porous sets

Michael Hrušák and Ondřej Zindulka

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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.

Article information

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

Dates
First available in Project Euclid: 20 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1327068697

Digital Object Identifier
doi:10.2178/jsl/1327068697

Mathematical Reviews number (MathSciNet)
MR2951635

Zentralblatt MATH identifier
1245.28003

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

Keywords
σ-monotone σ-porous cardinal invariants

Citation

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. https://projecteuclid.org/euclid.jsl/1327068697


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