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

# 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