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A dichotomy for P-ideals of countable sets. (English) Zbl 0968.03049

Summary: 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 \({\mathcal P}({\mathbb N})/\text{fin}\) but also on some higher order statements like for example the existence of Jensen square sequences.

MSC:

03E05 Other combinatorial set theory
03E35 Consistency and independence results
03E65 Other set-theoretic hypotheses and axioms
03E50 Continuum hypothesis and Martin’s axiom
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