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