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