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