### Archives

### 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

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

# 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

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