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