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P-Ideal Dichotomy 54G20 Absoluteness Poset Generalized Clubs Precaliber incompactness Well-behaved magma Monotonically far Cohen real strongly bounded groups free Boolean algebra Uniformly coherent Parameterized proxy principle Erdos Cardinal Non-saturation indecomposable filter Dushnik-Miller coloring number HOD Uniformly homogeneous nonmeager set Postprocessing function Sakurai's Bell inequality diamond star Ostaszewski square Luzin set Uniformization AIM forcing sap Ascent Path Sigma-Prikry OCA Successor of Regular Cardinal approachability ideal Erdos-Hajnal graphs middle diamond Slim tree Distributive tree very good scale regressive Souslin tree Large Cardinals b-scale Strongly Luzin set Square-Brackets Partition Relations Prikry-type forcing Entangled linear order C-sequence Small forcing Open Access Intersection model Greatly Mahlo L-space Hindman's Theorem Countryman line weak square club_AD Foundations xbox Rock n' Roll Singular cofinality Nonspecial tree Sierpinski's onto mapping principle weak diamond Generalized descriptive set theory projective Boolean algebra Strongly compact cardinal Cardinal function Interval topology on trees Martin's Axiom Iterated forcing Fast club Diamond weak Kurepa tree Prevalent singular cardinals Diamond-sharp stationary reflection Weakly compact cardinal perfectly normal Baumgartner's square Amenable C-sequence Almost countably chromatic Kurepa Hypothesis higher Baire space Cardinal Invariants stationary hitting PFA(S)[S] polarized partition relation Ascending path Coherent tree tensor product graph ZFC construction Filter reflection Singular Density Chang's conjecture S-Space Knaster Minimal Walks Commutative projection system Reflecting stationary set Reduced Power Fat stationary set Local Club Condensation. Subadditive Club Guessing Forcing Axiom R Forcing with side conditions Commutative cancellative semigroups Analytic sets stick Antichain SNR ccc Constructible Universe super-Souslin tree Lipschitz reduction Subtle tree property Singular cardinals combinatorics Diamond for trees Selective Ultrafilter Was Ulam right? reflection principles Microscopic Approach Fodor-type reflection Ineffable cardinal Closed coloring Partition Relations Forcing Axioms Ramsey theory over partitions positive partition relation Partition relations for trees Respecting tree unbounded function O-space Strong coloring Chromatic number Subnormal ideal Mandelbrot set Hereditarily Lindelöf space Dowker space square Whitehead Problem PFA specializable Souslin tree Rado's conjecture transformations Subtle cardinal full tree Hedetniemi's conjecture Ulam matrix Almost-disjoint family Aronszajn tree Successor of Singular Cardinal free Souslin tree Rainbow sets square principles GMA Almost Souslin Universal Sequences Souslin Tree countably metacompact Knaster and friends Shelah's Strong Hypothesis Vanishing levels Jonsson cardinal
Tag Archives: Partition relations for trees
Partition relations for trees II: Entangled linear orders
Joint work with Tanmay Inamdar. Abstract. We find new sufficient conditions for the existence of entangled linear orders. The constructions use anti-Ramsey colourings for trees, and they provide a fine control on the extent of entangledness. As an application, from … Continue reading
Posted in Partition Relations, Preprints
Tagged Aronszajn tree, Entangled linear order, Partition relations for trees, Strongly Luzin set
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Partition relations for trees I: Incomparable trees
Joint work with Tanmay Inamdar. Abstract. Todorcevic proved that Martin’s axiom implies that every two coherent $\aleph_1$-Aronszajn trees are comparable. Here, from cardinal arithmetic assumptions, we obtain the failure of the analogous statement for higher trees. In particular, for every … Continue reading
Posted in Partition Relations, Publications
Tagged Lipschitz reduction, Partition relations for trees
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Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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