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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

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

# 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