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