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