### Archives

### Recent blog posts

- 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

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

# 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