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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

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

# 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