### Archives

### Recent blog posts

- 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

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

# Tag Archives: Cohen real

## 6th European Set Theory Conference, July 2017

I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two $\kappa$-cc partial orders again $\kappa$-cc? Does there exist … Continue reading

Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
4 Comments

## 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