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