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