### 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

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

# 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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