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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

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

# 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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