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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

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

# 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