# A dichotomy for P-ideals of countable sets

Fundamenta Mathematicae (2000)

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

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topTodorčević, 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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- [6] R. Laver, Making supercompactness indestructible under κ-directed forcing, Israel J. Math. 29 (1978), 385-388. Zbl0381.03039
- [7] S. Shelah, Proper Forcing, Springer, 1982.
- [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] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294. Zbl0658.03028
- [10] S. Todorčević, Partition Problems in Topology, Amer. Math. Soc., Providence, 1989. Zbl0659.54001
- [11] S. Todorčević, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993), 130-167.

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