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 |