Totally proper forcing and the Moore–Mrówka problem

Volume 177 / 2003

Todd Eisworth Fundamenta Mathematicae 177 (2003), 121-137 MSC: Primary 03E75. DOI: 10.4064/fm177-2-2


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 ${\rm ZFC}+{\rm CH}$ 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.


  • Todd EisworthDepartment of Mathematics
    University of Northern Iowa
    Cedar Falls, IA 50614, U.S.A.

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