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