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Singular cofinality P-Ideal Dichotomy Poset Sakurai's Bell inequality Strong coloring stick Strongly Luzin set Hedetniemi's conjecture tensor product graph weak diamond Analytic sets diamond star Large Cardinals Forcing with side conditions Strongly compact cardinal indecomposable filter Partition relations for trees Chang's conjecture Subnormal ideal Generalized Clubs Erdos-Hajnal graphs regressive Souslin tree Weakly compact cardinal Diamond for trees middle diamond Slim tree Respecting tree Distributive tree Erdos Cardinal Partition Relations PFA(S)[S] Reduced Power Almost-disjoint family Dushnik-Miller Commutative projection system Hindman's Theorem Ineffable cardinal xbox Monotonically far unbounded function free Boolean algebra reflection principles Ulam matrix Souslin Tree Chromatic number square Successor of Regular Cardinal Coherent tree C-sequence weak Kurepa tree Whitehead Problem Rainbow sets nonmeager set free Souslin tree Cohen real full tree Square-Brackets Partition Relations stationary hitting OCA Rado's conjecture Aronszajn tree Shelah's Strong Hypothesis Reflecting stationary set countably metacompact Generalized descriptive set theory Commutative cancellative semigroups approachability ideal Sigma-Prikry Successor of Singular Cardinal coloring number positive partition relation Forcing Axioms sap projective Boolean algebra Forcing Cardinal Invariants Countryman line Martin's Axiom Local Club Condensation. Prikry-type forcing Ramsey theory over partitions Foundations SNR S-Space Nonspecial tree Fodor-type reflection Intersection model Diamond Universal Sequences Non-saturation Hereditarily Lindelöf space ZFC construction weak square Lipschitz reduction Interval topology on trees Uniformly coherent Singular cardinals combinatorics Sierpinski's onto mapping principle HOD Rock n' Roll polarized partition relation Axiom R square principles Kurepa Hypothesis club_AD Amenable C-sequence GMA L-space 54G20 Prevalent singular cardinals perfectly normal Club Guessing ccc transformations b-scale Vanishing levels PFA higher Baire space super-Souslin tree specializable Souslin tree incompactness AIM forcing Subadditive Almost countably chromatic very good scale Was Ulam right? Subtle tree property Cardinal function Diamond-sharp Fast club Mandelbrot set Selective Ultrafilter Constructible Universe Ascending path Jonsson cardinal strongly bounded groups Ascent Path Knaster and friends Subtle cardinal Entangled linear order Minimal Walks Antichain Filter reflection Dowker space stationary reflection Knaster Fat stationary set Parameterized proxy principle Well-behaved magma O-space Absoluteness Closed coloring Almost Souslin Uniformly homogeneous Ostaszewski square Open Access Uniformization Microscopic Approach Precaliber Luzin set Small forcing Greatly Mahlo Singular Density Postprocessing function Iterated forcing
Category Archives: Preprints
Partition relations for trees I: Incomparable trees
Joint work with Tanmay Inamdar. Abstract. Todorcevic proved that Martin’s axiom implies that every two coherent $\aleph_1$-Aronszajn trees are comparable. Here, from cardinal arithmetic assumptions, we obtain the failure of the analogous statement for higher trees. In particular, for every … Continue reading
Posted in Partition Relations, Preprints
Tagged Lipschitz reduction, Partition relations for trees
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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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