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