A dichotomy for P-ideals of countable sets

• Autorzy: Stevo Todorčević
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E65: Other hypotheses and axioms
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 166
• Numer: 3
• Strony: 251-267

Daty

wydano

2000

otrzymano

1999-11-17

Twórcy

autor

Stevo Todorčević

• Université Paris 7, C.N.R.S., UPRESA 7056, 2, Place Jussieu, 72251 Paris Cedex 05, France

Bibliografia

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• [5] R. B. Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229-308.
• [6] R. Laver, Making supercompactness indestructible under κ-directed forcing, Israel J. Math. 29 (1978), 385-388.
• [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.
• [10] S. Todorčević, Partition Problems in Topology, Amer. Math. Soc., Providence, 1989.
• [11] S. Todorčević, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993), 130-167.