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