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- 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

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

# Category Archives: Topology

## 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

## A topological reflection principle equivalent to Shelah’s strong hypothesis

Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading

Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Shelah's Strong Hypothesis
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