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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

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

# 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