A dichotomy for P-ideals of countable sets

Stevo Todorčević

Fundamenta Mathematicae (2000)

  • Volume: 166, Issue: 3, page 251-267
  • ISSN: 0016-2736

Abstract

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A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra P ( ℕ ) / but also on some higher order statements like for example the existence of Jensen square sequences.

How to cite

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Todorčević, Stevo. "A dichotomy for P-ideals of countable sets." Fundamenta Mathematicae 166.3 (2000): 251-267. <http://eudml.org/doc/212480>.

@article{Todorčević2000,
abstract = {A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra $P(\mathbb \{N\})$/ but also on some higher order statements like for example the existence of Jensen square sequences.},
author = {Todorčević, Stevo},
journal = {Fundamenta Mathematicae},
keywords = {continuum hypothesis; ideals of countable sets},
language = {eng},
number = {3},
pages = {251-267},
title = {A dichotomy for P-ideals of countable sets},
url = {http://eudml.org/doc/212480},
volume = {166},
year = {2000},
}

TY - JOUR
AU - Todorčević, Stevo
TI - A dichotomy for P-ideals of countable sets
JO - Fundamenta Mathematicae
PY - 2000
VL - 166
IS - 3
SP - 251
EP - 267
AB - A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra $P(\mathbb {N})$/ but also on some higher order statements like for example the existence of Jensen square sequences.
LA - eng
KW - continuum hypothesis; ideals of countable sets
UR - http://eudml.org/doc/212480
ER -

References

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  1. [1] U. Abraham and S. Todorčević, Partition properties of ω 1 compatible with CH, Fund. Math. 152 (1997), 165-181. Zbl0879.03015
  2. [2] K. J. Devlin, The Yorkshireman's guide to proper forcing, in: Surveys in Set Theory, A. R. D. Mathias (ed.), Cambridge Univ. Press, 1983, 60-105. 
  3. [3] F. Hausdorff, Summen von ℵ 1 Mengen, Fund. Math. 26 (1936), 241-255. 
  4. [4] J. Hirschorn, Random trees under CH, preprint, 1999. 
  5. [5] R. B. Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229-308. Zbl0257.02035
  6. [6] R. Laver, Making supercompactness indestructible under κ-directed forcing, Israel J. Math. 29 (1978), 385-388. Zbl0381.03039
  7. [7] S. Shelah, Proper Forcing, Springer, 1982. 
  8. [8] S. Todorčević, Trees and linearly ordered sets, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 235-293. 
  9. [9] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294. Zbl0658.03028
  10. [10] S. Todorčević, Partition Problems in Topology, Amer. Math. Soc., Providence, 1989. Zbl0659.54001
  11. [11] S. Todorčević, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993), 130-167. 

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