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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

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

# 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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