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