### Archives

### Recent blog posts

- 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
- PFA and the tree property at $\aleph_2$ June 9, 2013

### Keywords

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

- Luzin sets and generalizations
- Nonuniversal colorings in ZFC
- Large Sets
- Infinite-dimensional Jonsson algebras
- Strong colorings without nontrivial polychromatic sets
- Infinite-dimensional polychromatic colorings
- Polychromatic colorings of the first uncountable cardinal
- From colorings to topology
- From topology to colorings
- Anti-Ramsey colorings of the rational numbers, part 2

# 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