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