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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
- Genearlizations 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

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

# 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