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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

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

# 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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