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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

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

# Tag Archives: Singular Density

## 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

## 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

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading