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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

Rainbow sets middle diamond weak diamond 05D10 Jonsson cardinal Hindman's Theorem Singular coﬁnality Kurepa Hypothesis OCA Nonspecial tree Forcing Axioms Rado's conjecture Chang's conjecture Universal Sequences Singular cardinals combinatorics square principles Shelah's Strong Hypothesis square approachability ideal Prevalent singular cardinals Generalized Clubs sap Successor of Singular Cardinal Parameterized proxy principle PFA(S)[S] stationary hitting Square-Brackets Partition Relations 11P99 Aronszajn tree Erdos Cardinal Ascent Path polarized partition relation Almost countably chromatic Uniformly coherent Hedetniemi's conjecture coloring number projective Boolean algebra Poset Constructible Universe HOD Uniformization Souslin Tree Axiom R Cardinal function Postprocessing function incompactness Successor of Regular Cardinal Coherent tree Mandelbrot set reflection principles Partition Relations Slim tree Microscopic Approach very good scale xbox Reduced Power Ostaszewski square Stevo Todorcevic Fast club Antichain Almost Souslin Fodor-type reflection Selective Ultrafilter Forcing Almost-disjoint famiy stationary reflection Sakurai's Bell inequality weak square PFA Knaster Club Guessing Diamond Rock n' Roll free Boolean algebra Small forcing Hereditarily Lindelöf space Cohen real Singular Density Foundations b-scale diamond star Prikry-type forcing Minimal Walks ccc Whitehead Problem Dushnik-Miller Distributive tree Fat stationary set 20M14 S-Space Cardinal Invariants L-space Commutative cancellative semigroups P-Ideal Dichotomy Absoluteness Erdos-Hajnal graphs Weakly compact cardinal Chromatic number 05A17 tensor product graph Martin's Axiom Non-saturation Large Cardinals

# 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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