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coloring number C-sequence Successor of Regular Cardinal 54G20 Martin's Axiom Coherent tree Precaliber OCA Souslin Tree Well-behaved magma L-space Vanishing levels Selective Ultrafilter Successor of Singular Cardinal nonmeager set Chang's conjecture AIM forcing Subtle cardinal Erdos Cardinal Hereditarily Lindelöf space b-scale full tree Rado's conjecture ccc Sierpinski's onto mapping principle Luzin set projective Boolean algebra HOD S-Space Ascent Path stick reflection principles Antichain Ramsey theory over partitions Generalized descriptive set theory Strong coloring Local Club Condensation. Forcing club_AD approachability ideal O-space higher Baire space Greatly Mahlo free Boolean algebra Nonspecial tree Strongly Luzin set Ostaszewski square Parameterized proxy principle Amenable C-sequence stationary hitting Weakly compact cardinal SNR Square-Brackets Partition Relations regressive Souslin tree diamond star Dowker space Diamond-sharp Slim tree P-Ideal Dichotomy specializable Souslin tree Singular cofinality Large Cardinals Distributive tree transformations Hindman's Theorem tensor product graph Open Access incompactness Singular cardinals combinatorics Uniformly coherent Sakurai's Bell inequality Hedetniemi's conjecture Prikry-type forcing Closed coloring Sigma-Prikry Minimal Walks Lipschitz reduction sap Small forcing positive partition relation Shelah's Strong Hypothesis Chromatic number Constructible Universe super-Souslin tree Fast club Diamond free Souslin tree Fat stationary set very good scale Iterated forcing Uniformly homogeneous Generalized Clubs Almost Souslin Fodor-type reflection Poset Knaster and friends Was Ulam right Almost countably chromatic square principles Almost-disjoint family Subnormal ideal Absoluteness Uniformization Cardinal Invariants Postprocessing function weak square Ulam matrix Subadditive weak diamond middle diamond Mandelbrot set Erdos-Hajnal graphs xbox countably metacompact Reflecting stationary set Dushnik-Miller GMA ZFC construction Cohen real Aronszajn tree Subtle tree property stationary reflection PFA(S)[S] Rainbow sets PFA Foundations Filter reflection polarized partition relation Partition Relations Universal Sequences Ineffable cardinal Whitehead Problem Prevalent singular cardinals Rock n' Roll Microscopic Approach Axiom R Diamond for trees Singular Density unbounded function Non-saturation Club Guessing indecomposable ultrafilter Cardinal function strongly bounded groups weak Kurepa tree square Analytic sets Knaster Commutative cancellative semigroups Forcing Axioms Reduced Power Jonsson cardinal Kurepa Hypothesis
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, Open Access, Shelah's Strong Hypothesis
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