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### 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

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

# 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
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## 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