### 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

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

# 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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