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