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