### 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

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

# Tag Archives: Prevalent singular cardinals

## 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

## Singular Cardinal Combinatorics and Inner Model Theory

These are the slides of a talk given at the Singular Cardinal Combinatorics and Inner Model Theory conference (Gainesville, 5–9 March 2007). Talk Title: Antichains in partially ordered sets of singular cofinality Abstract: We say that a singular cardinal $\lambda$ is a prevalent singular … 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