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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Distributive tree Kurepa Hypothesis Knaster square principles Constructible Universe xbox Uniformization Luzin set Diamond weak square Hindman's Theorem Singular Density Erdos-Hajnal graphs Cohen real Selective Ultrafilter ccc Reduced Power Mandelbrot set stationary reflection Non-saturation Poset very good scale stationary hitting HOD coloring number Forcing Axioms Prevalent singular cardinals Forcing Axiom R Successor of Singular Cardinal Dushnik-Miller Hedetniemi's conjecture Stevo Todorcevic Chromatic number Martin's Axiom Cardinal Invariants Almost countably chromatic Successor of Regular Cardinal Sakurai's Bell inequality Coherent tree Uniformly coherent polarized partition relation 05A17 PFA b-scale Fat stationary set Small forcing Singular coﬁnality sap projective Boolean algebra L-space Commutative cancellative semigroups Fodor-type reflection Rado's conjecture Souslin Tree Shelah's Strong Hypothesis reflection principles PFA(S)[S] diamond star Partition Relations middle diamond free Boolean algebra Erdos Cardinal 11P99 Club Guessing approachability ideal Universal Sequences Cardinal function Antichain Almost-disjoint famiy super-Souslin tree Minimal Walks weak diamond Large Cardinals Weakly compact cardinal Ascent Path Hereditarily Lindelöf space 20M14 Ostaszewski square Nonspecial tree Rock n' Roll Prikry-type forcing Aronszajn tree Foundations P-Ideal Dichotomy Parameterized proxy principle Rainbow sets Absoluteness Microscopic Approach OCA Slim tree Square-Brackets Partition Relations square Chang's conjecture incompactness Almost Souslin Singular cardinals combinatorics Postprocessing function Whitehead Problem tensor product graph Generalized Clubs S-Space Fast club Jonsson cardinal

# Tag Archives: PFA(S)[S]

## 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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