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Recent blog posts
- The S-space problem, and the cardinal invariant $\mathfrak b$ April 4, 2013
- An $S$-space from a Cohen real April 3, 2013
- Forcing with a Souslin tree makes $\mathfrak p=\omega_1$ April 1, 2013
- The S-space problem, and the cardinal invariant $\mathfrak p$ March 28, 2013
- Jones’ theorem on the cardinal invariant $\mathfrak p$ March 26, 2013
- Erdős 100 March 26, 2013
- Bell’s theorem on the cardinal invariant $\mathfrak p$ March 21, 2013
- The $\Delta$-system lemma: an elementary proof March 20, 2013
Keywords
Erdos-Hajnal graphs Diamond Singular Cofinality Shelah's Strong Hypothesis Rainbow sets Foundations polarized partition relation PFA(S)[S] Kurepa Hypothesis Large Cardinals S-Space Club Guessing Prevalent singular cardinals Partition Relations very good scale Dushnik-Miller P-Ideal Dichotomy incompactness Square-Brackets Partition Relations Prikry-type forcing middle diamond Cohen real diamond star Cardinal function Aronszajn tree Uniformization Sakurai's Bell inequality Souslin Tree Mandelbrot set Forcing Successor of Singular Cardinal Erdos Cardinal Whitehead Problem Non-saturation Rado's conjecture approachability ideal Chromatic number Poset Ostaszewski square Small forcing Axiom R square Hereditarily Lindelöf space Singular Density free Boolean algebra Antichain reflection principles Minimal Walks Generalized Clubs Knaster Singular cardinals combinatorics Almost countably chromatic Rock n' Roll stationary reflection stationary hitting Successor of Regular Cardinal sap weak square b-scale weak diamond projective Boolean algebra
Tag Archives: Hereditarily Lindelöf space
The S-space problem, and the cardinal invariant $\mathfrak p$
Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. Do they exist? Consistently, yes. However, Szentmiklóssy proved that compact $S$-spaces do not exist, assuming Martin’s Axiom. Pushing this further, Todorcevic later proved that … Continue reading
Posted in Blog, Expository, Open Problems
Tagged Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
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On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
Workshop on Set Theory and its Applications
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading
