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