### 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
- 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

### Keywords

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

# Tag Archives: Cardinal function

## 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

## Infinite Combinatorial Topology

Back in 2005, as a master student, I attended a course by Boaz Tsaban, entitled “Infinite Combinatorial Topology”. A friend and I decided to produce lecture notes, but in a somewhat loose sense, that is: we sometimes omit material given … Continue reading

Posted in Notes
Tagged b-scale, Cardinal function, Cardinal Invariants, Hereditarily Lindelöf space
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