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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

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

# 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