### Archives

### Recent blog posts

- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

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

# 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