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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

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

# 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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