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- 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

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

# 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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