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