### Archives

### 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

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

# 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