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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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
4 Comments

## The S-space problem, and the cardinal invariant $\mathfrak p$

Posted in Blog, Expository, Open Problems
Tagged Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
4 Comments