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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

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

# 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