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Poset Forcing Generalized Clubs Singular coﬁnality Non-saturation square principles Uniformly coherent weak diamond Uniformization Minimal Walks Rado's conjecture projective Boolean algebra Erdos Cardinal Weakly compact cardinal Shelah's Strong Hypothesis tensor product graph Club Guessing Selective Ultrafilter Successor of Regular Cardinal weak square reflection principles 11P99 Absoluteness b-scale Rainbow sets Rock n' Roll PFA polarized partition relation very good scale Sakurai's Bell inequality Ostaszewski square ccc S-Space Erdos-Hajnal graphs Square-Brackets Partition Relations Partition Relations Antichain Foundations Aronszajn tree coloring number Prikry-type forcing PFA(S)[S] Hindman's Theorem Universal Sequences Dushnik-Miller Almost Souslin incompactness Ascent Path Almost countably chromatic 05A17 Prevalent singular cardinals square OCA Almost-disjoint famiy middle diamond Commutative cancellative semigroups diamond star Stevo Todorcevic Mandelbrot set L-space Souslin Tree stationary hitting Slim tree free Boolean algebra 05D10 Parameterized proxy principle HOD Knaster Fast club Singular cardinals combinatorics Distributive tree Jonsson cardinal Small forcing Cardinal function Martin's Axiom Constructible Universe Diamond Cardinal Invariants Fodor-type reflection Cohen real xbox Whitehead Problem Successor of Singular Cardinal approachability ideal sap Nonspecial tree Postprocessing function stationary reflection Chromatic number Kurepa Hypothesis Forcing Axioms 20M14 Hedetniemi's conjecture Chang's conjecture Reduced Power P-Ideal Dichotomy Axiom R Coherent tree Fat stationary set Microscopic Approach Singular Density Large Cardinals Hereditarily Lindelöf space

# 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
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