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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
- 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

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

# 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, March 2007

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, 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