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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
- 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

### Keywords

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

# 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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