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- 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

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

# 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