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### Recent blog posts

- 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

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

# 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