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