Totally proper forcing and the Moore–Mrówka problem
Copyright policy )Totally proper forcing and the Moore–Mrówka problem
Summary: We describe a totally proper notion of forcing that can be used to shoot uncountable free sequences through certain countably compact non-compact spaces. This is almost (but not quite!) enough to produce a model of \(\text{ZFC}+\text{CH}\) in which countably tight compact spaces are sequential -- we still do not know if the notion of forcing described in the paper can be iterated without adding reals.
- University of Northern Colorado United States
continuum hypothesis, Consistency and independence results in general topology, totally proper forcing, Compactness, Continuum hypothesis and Martin's axiom, Applications of set theory, Consistency and independence results, compact space, sequential space, countable tightness
continuum hypothesis, Consistency and independence results in general topology, totally proper forcing, Compactness, Continuum hypothesis and Martin's axiom, Applications of set theory, Consistency and independence results, compact space, sequential space, countable tightness
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