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