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Square-Brackets Partition Relations Nonspecial tree Prikry-type forcing Universal Sequences Ulam matrix projective Boolean algebra Lipschitz reduction Iterated forcing Parameterized proxy principle Strongly Luzin set Erdos-Hajnal graphs Dowker space Postprocessing function Luzin set Sakurai's Bell inequality Diamond-sharp Uniformly homogeneous 54G20 Hedetniemi's conjecture Knaster and friends Microscopic Approach Distributive tree Absoluteness diamond star Subadditive P-Ideal Dichotomy Cardinal function indecomposable filter Souslin Tree Well-behaved magma Diamond for trees ccc transformations Selective Ultrafilter Shelah's Strong Hypothesis AIM forcing Cohen real Diamond Entangled linear order weak square Hindman's Theorem Countryman line Large Cardinals Rainbow sets reflection principles Aronszajn tree Antichain club_AD stick nonmeager set coloring number Singular cardinals combinatorics Coherent tree OCA Ineffable cardinal Closed coloring Strongly compact cardinal S-Space Successor of Regular Cardinal Open Access SNR strongly bounded groups C-sequence Almost Souslin Subtle tree property Singular cofinality Club Guessing countably metacompact Hereditarily Lindelöf space Interval topology on trees full tree approachability ideal very good scale Almost-disjoint family free Souslin tree Ostaszewski square Partition relations for trees Almost countably chromatic Whitehead Problem Precaliber Commutative cancellative semigroups Fat stationary set weak diamond Generalized descriptive set theory Chromatic number Intersection model Uniformization regressive Souslin tree Generalized Clubs Jonsson cardinal Foundations Kurepa Hypothesis Forcing specializable Souslin tree Uniformly coherent Fast club Was Ulam right? Sigma-Prikry Axiom R L-space Non-saturation Filter reflection Fodor-type reflection square principles Ascending path Local Club Condensation. Rado's conjecture stationary reflection Partition Relations Martin's Axiom Monotonically far GMA xbox Dushnik-Miller Constructible Universe Small forcing Analytic sets free Boolean algebra Ramsey theory over partitions square Chang's conjecture Weakly compact cardinal HOD O-space Ascent Path stationary hitting incompactness Rock n' Roll Mandelbrot set super-Souslin tree Amenable C-sequence Minimal Walks Slim tree PFA Reflecting stationary set middle diamond Subnormal ideal Forcing Axioms sap ZFC construction Successor of Singular Cardinal perfectly normal Greatly Mahlo Poset Forcing with side conditions tensor product graph b-scale weak Kurepa tree Subtle cardinal Strong coloring unbounded function higher Baire space Commutative projection system Knaster polarized partition relation positive partition relation Sierpinski's onto mapping principle Singular Density Prevalent singular cardinals Erdos Cardinal Respecting tree Vanishing levels Reduced Power PFA(S)[S] Cardinal Invariants
Category Archives: Preprints
Partition relations for trees II: Entangled linear orders
Joint work with Tanmay Inamdar. Abstract. We find new sufficient conditions for the existence of entangled linear orders. The constructions use anti-Ramsey colourings for trees, and they provide a fine control on the extent of entangledness. As an application, from … Continue reading
Posted in Partition Relations, Preprints
Tagged Aronszajn tree, Entangled linear order, Partition relations for trees, Strongly Luzin set
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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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Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … Continue reading
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … Continue reading
The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$. In addition, … Continue reading
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Open Access, Prikry-type forcing, ZFC construction
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