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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
- 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

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

# Tag Archives: Hereditarily Lindelöf space

## The S-space problem, and the cardinal invariant $\mathfrak p$

Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. Do they exist? Consistently, yes. However, Szentmiklóssy proved that compact $S$-spaces do not exist, assuming Martin’s Axiom. Pushing this further, Todorcevic later proved that … Continue reading

Posted in Blog, Expository, Open Problems
Tagged Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
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## 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

## Workshop on Set Theory and its Applications

These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … 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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