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- 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

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

# 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