### 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

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