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