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Almost-disjoint family Subtle tree property GMA Rainbow sets xbox sap Dushnik-Miller Hedetniemi's conjecture Intersection model Forcing Axioms Sakurai's Bell inequality Knaster and friends Reflecting stationary set PFA higher Baire space Interval topology on trees Minimal Walks PFA(S)[S] 54G20 Knaster S-Space positive partition relation polarized partition relation Shelah's Strong Hypothesis Foundations Subnormal ideal middle diamond Commutative projection system Mandelbrot set Luzin set Filter reflection Non-saturation Subtle cardinal very good scale Cardinal function Fat stationary set Almost Souslin nonmeager set Large Cardinals Whitehead Problem Aronszajn tree Successor of Singular Cardinal Absoluteness approachability ideal Forcing with side conditions Ostaszewski square square Uniformization Strongly Luzin set Ascent Path Slim tree Chromatic number ZFC construction weak Kurepa tree Square-Brackets Partition Relations SNR Countryman line club_AD Souslin Tree strongly bounded groups Rock n' Roll Diamond Fast club OCA diamond star reflection principles Club Guessing stationary hitting Ulam matrix Prevalent singular cardinals square principles Well-behaved magma Cardinal Invariants Prikry-type forcing P-Ideal Dichotomy super-Souslin tree Poset Singular cardinals combinatorics Parameterized proxy principle regressive Souslin tree tensor product graph Distributive tree Generalized Clubs Uniformly coherent full tree Subadditive Nonspecial tree O-space unbounded function perfectly normal Sierpinski's onto mapping principle Local Club Condensation. Lipschitz reduction projective Boolean algebra b-scale Entangled linear order L-space Strong coloring Partition relations for trees weak square free Souslin tree Selective Ultrafilter HOD Constructible Universe Reduced Power stationary reflection Commutative cancellative semigroups Amenable C-sequence Ramsey theory over partitions ccc weak diamond Fodor-type reflection Erdos-Hajnal graphs Kurepa Hypothesis Dowker space Monotonically far Forcing AIM forcing Was Ulam right? Jonsson cardinal indecomposable filter Singular Density transformations Greatly Mahlo stick Postprocessing function Small forcing Iterated forcing Open Access Sigma-Prikry Ascending path Axiom R Hereditarily Lindelöf space Respecting tree Hindman's Theorem Ineffable cardinal Almost countably chromatic Strongly compact cardinal Partition Relations Coherent tree coloring number Successor of Regular Cardinal Erdos Cardinal Analytic sets Microscopic Approach Rado's conjecture Weakly compact cardinal Diamond-sharp Universal Sequences specializable Souslin tree Chang's conjecture Diamond for trees Cohen real Generalized descriptive set theory Singular cofinality Antichain free Boolean algebra Martin's Axiom countably metacompact C-sequence Closed coloring Uniformly homogeneous incompactness Precaliber Vanishing levels
Tag Archives: Countryman line
MFO workshop in Set Theory, January 2025
I gave an invited talk at the Set Theory meeting in Obwerwolfach, January 2025. Talk Title: Non-structure theorems for higher Aronszajn lines. Abstract: An $\omega_1$-Countryman line is an uncountable linear order $L$ such that $L^2$ (with the pointwise ordering) is … Continue reading
Posted in Invited Talks
Tagged Countryman line, Monotonically far
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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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