Luzin and anti-Luzin almost disjoint families

Judith Roitman; Lajos Soukup

Fundamenta Mathematicae (1998)

  • Volume: 158, Issue: 1, page 51-67
  • ISSN: 0016-2736

Abstract

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Under M A ω 1 every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.

How to cite

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Roitman, Judith, and Soukup, Lajos. "Luzin and anti-Luzin almost disjoint families." Fundamenta Mathematicae 158.1 (1998): 51-67. <http://eudml.org/doc/212302>.

@article{Roitman1998,
abstract = {Under $MA_\{ω_1\}$ every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.},
author = {Roitman, Judith, Soukup, Lajos},
journal = {Fundamenta Mathematicae},
keywords = {Luzin; almost disjoint family; Luzin families; almost disjoint families},
language = {eng},
number = {1},
pages = {51-67},
title = {Luzin and anti-Luzin almost disjoint families},
url = {http://eudml.org/doc/212302},
volume = {158},
year = {1998},
}

TY - JOUR
AU - Roitman, Judith
AU - Soukup, Lajos
TI - Luzin and anti-Luzin almost disjoint families
JO - Fundamenta Mathematicae
PY - 1998
VL - 158
IS - 1
SP - 51
EP - 67
AB - Under $MA_{ω_1}$ every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.
LA - eng
KW - Luzin; almost disjoint family; Luzin families; almost disjoint families
UR - http://eudml.org/doc/212302
ER -

References

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  1. [AT] U. Abraham and S. Todorčević, Partition properties of ω 1 compatible with CH, Fund. Math. 152 (1997), 165-181. Zbl0879.03015
  2. [EF] F. Eckertson, W. Fleissner, A. Korovin and R. Levy, Not realcompact images of not Lindelöf spaces, Topology Appl. 58 (1994), 115-125. Zbl0819.54003
  3. [HJ] A. Hajnal and I. Juhász, Intersection properties of open sets, ibid. 19 (1985), 201-209. Zbl0582.54003
  4. [JN] I. Juhász, Zs. Nagy, L. Soukup and Z. Szentmiklóssy, Intersection properties of open sets, II, in: Papers on General Topology and Applications, Proc. 10th Summer Conference in General Topology and Applications, 1994, E. Coplakova and K. P. Hart (eds.), Ann. New York Acad. Sci. 788, New York Acad. Sci., 1996, 147-159. Zbl0919.54005
  5. [JS] I. Juhász, L. Soukup and Z. Szentmiklóssy, Combinatorial principles from adding Cohen reals, in: Logic Colloquium 95, Haifa, to appear. Zbl0896.03039
  6. [K] S. Koppelberg, Handbook of Boolean Algebras, Vol. I, North-Holland, Amsterdam, 1987. 
  7. [L] N. Luzin, On parts of the natural series, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 403-410 (in Russian). 
  8. [V] B. Velickovic, OCA and automorphisms of P(ω)/fin, Topology Appl. 49 (1993), 1-13. 

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