Archives
Keywords
transformations strongly bounded groups Jonsson cardinal Axiom R Non-saturation Lipschitz reduction Entangled linear order Forcing with side conditions weak diamond countably metacompact Universal Sequences Rainbow sets Luzin set Vanishing levels weak Kurepa tree Constructible Universe reflection principles nonmeager set projective Boolean algebra Well-behaved magma C-sequence Whitehead Problem Successor of Singular Cardinal SNR Filter reflection S-Space Fat stationary set indecomposable filter Absoluteness Hereditarily Lindelöf space Precaliber Strongly Luzin set Small forcing Antichain b-scale Successor of Regular Cardinal Fast club Monotonically far Rado's conjecture Partition Relations Almost-disjoint family club_AD incompactness Cohen real Strong coloring middle diamond Square-Brackets Partition Relations free Boolean algebra Forcing Hindman's Theorem Diamond OCA Selective Ultrafilter HOD Subtle cardinal Martin's Axiom Large Cardinals Mandelbrot set Commutative cancellative semigroups perfectly normal Open Access weak square Weakly compact cardinal unbounded function Diamond for trees Analytic sets ccc regressive Souslin tree very good scale sap Uniformly coherent Foundations Coherent tree Ineffable cardinal Was Ulam right? O-space Ramsey theory over partitions Strongly compact cardinal Chang's conjecture Subadditive full tree Amenable C-sequence PFA(S)[S] Club Guessing Uniformization stick Diamond-sharp Shelah's Strong Hypothesis Fodor-type reflection Uniformly homogeneous free Souslin tree Knaster specializable Souslin tree Distributive tree stationary reflection Sakurai's Bell inequality Aronszajn tree Commutative projection system Reflecting stationary set square principles Almost Souslin Cardinal Invariants Almost countably chromatic positive partition relation Chromatic number Singular cardinals combinatorics Reduced Power Cardinal function stationary hitting Erdos Cardinal Minimal Walks P-Ideal Dichotomy Erdos-Hajnal graphs Sigma-Prikry Parameterized proxy principle Subtle tree property xbox Closed coloring Iterated forcing higher Baire space Hedetniemi's conjecture ZFC construction Slim tree Sierpinski's onto mapping principle AIM forcing Ascent Path Rock n' Roll polarized partition relation Local Club Condensation. Singular cofinality coloring number PFA Subnormal ideal L-space diamond star Generalized descriptive set theory Souslin Tree Microscopic Approach super-Souslin tree Forcing Axioms Nonspecial tree Ostaszewski square GMA Prikry-type forcing Countryman line Interval topology on trees Dowker space Prevalent singular cardinals Poset Greatly Mahlo tensor product graph approachability ideal Kurepa Hypothesis Intersection model Singular Density Ascending path square Dushnik-Miller Respecting tree Postprocessing function Ulam matrix Generalized Clubs 54G20 Knaster and friends
Tag Archives: GMA
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
Joint work with Menachem Kojman and Juris Steprāns. Abstract. In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E17, 03E35, GMA, Martin's Axiom, positive partition relation, Ramsey theory over partitions
1 Comment
Generalizations of Martin’s Axiom and the well-met condition
Recall that Martin’s Axiom asserts that for every partial order $\mathbb P$ satisfying c.c.c., and for any family $\mathcal D$ of $<2^{\aleph_0}$ many dense subsets of $\mathbb P$, there exists a directed subset $G$ of $\mathbb P$ such that $G\cap … Continue reading
Posted in Blog, Expository
Tagged ccc, Forcing Axioms, GMA, Martin's Axiom, Uniformization
Leave a comment
