### 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

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

# 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