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- 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

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

# 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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