Countable tightness and proper forcing
نویسندگان
چکیده
منابع مشابه
First Countable Continua and Proper Forcing
Assuming the Continuum Hypothesis, there is a compact first countable connected space of weight א1 with no totally disconnected perfect subsets. Each such space, however, may be destroyed by some proper forcing order which does not add reals.
متن کاملPfa(s) and Countable Tightness
Todorcevic introduced the forcing axiom PFA(S) and established many consequences. We contribute to this project. In particular, we consider status under PFA(S) of two important consequences of PFA concerning spaces of countable tightness. In particular we prove that the existence of a Souslin tree does not imply the existence of a compact non-sequential space of countable tightness. We contrast...
متن کاملVariations on Countable Tightness
We consider 9 natural tightness conditions for topological spaces that are all variations on countable tightnes and investigate the interrelationships between them. Several natural open problems are raised.
متن کاملCountable Tightness, Elementary Submodels and Homogeneity
We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than 20 .
متن کاملOn Compact Hausdorff Spaces of Countable Tightness
A general combinatorial theorem for countably compact, noncompact spaces is given under the Proper Forcing Axiom. It follows that compact Hausdorff spaces of countable tightness are sequential under PFA, solving the Moore-Mrowka Problem. Other applications are also given.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1988
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1988-15649-2