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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 sigma-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) > sigma-linked, but non(Mon) < sigma-centered is consistent. Also cov(Mon) < c and cof(N) < cov(Mon) are consistent.
  • 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 sigma-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) > sigma-linked, but non(Mon) < sigma-centered is consistent. Also cov(Mon) < c and cof(N) < cov(Mon) are consistent. (en)
Title
  • Cardinal invariants of monotone and porous sets
  • Cardinal invariants of monotone and porous sets (en)
skos:prefLabel
  • Cardinal invariants of monotone and porous sets
  • Cardinal invariants of monotone and porous sets (en)
skos:notation
  • RIV/68407700:21110/12:00192533!RIV13-MSM-21110___
http://linked.open...avai/predkladatel
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  • Z(MSM6840770006)
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  • 1
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  • 125998
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  • RIV/68407700:21110/12:00192533
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  • sigma-monotone; sigma-porous; cardinal invariants (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [7CBC04834882]
http://linked.open...i/riv/nazevZdroje
  • Journal of Symbolic Logic
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  • 77
http://linked.open...iv/tvurceVysledku
  • Zindulka, Ondřej
  • Hrušák, M.
http://linked.open...ain/vavai/riv/wos
  • 000302526400010
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-4812
number of pages
http://bibframe.org/vocab/doi
  • 10.2178/jsl/1327068697
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  • 21110
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