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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

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

# 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
4 Comments

## 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, February 2007

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
8 Comments