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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
- Genearlizations 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

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

# Tag Archives: Cohen real

## An $S$-space from a Cohen real

Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. In this post, we shall establish the consistency of the existence of such a space. Theorem (Roitman, 1979). Let $\mathbb C=({}^{<\omega}\omega,\subseteq)$ be the notion of … Continue reading