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### Recent blog posts

- 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

square Slim tree Antichain Chang's conjecture Foundations Minimal Walks Almost countably chromatic Sakurai's Bell inequality 20M14 Postprocessing function b-scale Microscopic Approach Selective Ultrafilter Poset Martin's Axiom Fast club Cohen real Almost Souslin PFA(S)[S] Singular cardinals combinatorics Uniformly coherent Universal Sequences Absoluteness Singular coﬁnality tensor product graph Hereditarily Lindelöf space Partition Relations Parameterized proxy principle Commutative cancellative semigroups Shelah's Strong Hypothesis Chromatic number Forcing Axioms Successor of Regular Cardinal Knaster Constructible Universe Prikry-type forcing 11P99 Fat stationary set middle diamond Ascent Path square principles Distributive tree Souslin Tree Erdos Cardinal Erdos-Hajnal graphs S-Space ccc Club Guessing Reduced Power Hedetniemi's conjecture Aronszajn tree stationary reflection Non-saturation diamond star Cardinal function Almost-disjoint famiy reflection principles sap Generalized Clubs weak diamond Coherent tree Rado's conjecture Fodor-type reflection Jonsson cardinal coloring number Cardinal Invariants HOD Small forcing Kurepa Hypothesis OCA stationary hitting Square-Brackets Partition Relations P-Ideal Dichotomy 05D10 Nonspecial tree 05A17 very good scale weak square projective Boolean algebra Singular Density Prevalent singular cardinals Weakly compact cardinal Stevo Todorcevic Diamond Ostaszewski square Mandelbrot set L-space Rock n' Roll Uniformization Hindman's Theorem Rainbow sets Forcing Axiom R Large Cardinals free Boolean algebra approachability ideal xbox Successor of Singular Cardinal incompactness Whitehead Problem polarized partition relation PFA Dushnik-Miller

# Tag Archives: Singular Density

## On topological spaces of singular density and minimal weight

Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading

## Workshop on Set Theory and its Applications, February 2007

These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading