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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

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

# Tag Archives: Cohen real

## 6th European Set Theory Conference, July 2017

I gave a 3-lectures 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