### 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

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

# 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