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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

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

# 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
2 Comments