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Tight gaps in \({\mathcal P}(\omega)\). (English) Zbl 0840.03036

Summary: We prove some results on gaps in \({\mathcal P} (\omega)\). In particular we prove that the following statement is consistent: Every \(\subseteq^*\)-increasing \(\omega_1\)-sequence in \({\mathcal P} (\omega)\) is the bottom half of some tight \((\omega_1, \omega^*_2)\)-gap.

MSC:

03E05 Other combinatorial set theory
03E35 Consistency and independence results
03E50 Continuum hypothesis and Martin’s axiom