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

# 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