### 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
- Generalizations 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

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

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