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