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

# 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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