### Archives

### 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

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

# Tag Archives: 54G15

## 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 Publications, Topology
Tagged 03E04, 03E65, 54G15, Shelah's Strong Hypothesis
Leave a comment