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Cardinal invariants of monotone and porous sets

Published online by Cambridge University Press:  12 March 2014

Michael Hrušák  and
Ondřej Zindulka
Michael Hrušák
Affiliation:
Instituto De Matemáticas, Universidad Nacional Autonóma de México, Apartado Postal 61-3, Xangari, 58089, Morelia, Michoacán, México, E-mail: michael@matmor.unam.mx
Ondřej Zindulka
Affiliation:
Department of Mathematics, Faculty of Civil Engineering, Czech Technical University,Thákurova 7, 160 00 Prague 6, Czech Republic, E-mail: zindulka@mat.fsv.cvut.cz, URL: http://mat.fsv.cvut.cz/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.

Keywords

σ-monotoneσ-porouscardinal invariants
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 159 - 173
Copyright
Copyright © Association for Symbolic Logic 2012

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