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Ostaszewski square Small forcing Subadditive Cardinal Invariants Selective Ultrafilter Mandelbrot set Rado's conjecture Axiom R Postprocessing function HOD Subnormal ideal Amenable C-sequence Uniformly coherent Shelah's Strong Hypothesis OCA square Ineffable cardinal tensor product graph Local Club Condensation. Ascending path coloring number Almost countably chromatic Dushnik-Miller sap unbounded function Coherent tree Diamond Reflecting stationary set super-Souslin tree Singular cardinals combinatorics positive partition relation Uniformization Singular cofinality xbox Constructible Universe Strong coloring polarized partition relation Foundations stationary reflection PFA Subtle tree property stationary hitting Poset Nonspecial tree Interval topology on trees Generalized descriptive set theory Successor of Regular Cardinal AIM forcing nonmeager set Square-Brackets Partition Relations Fodor-type reflection Kurepa Hypothesis Microscopic Approach free Boolean algebra Uniformly homogeneous PFA(S)[S] Lipschitz reduction Entangled linear order higher Baire space Prevalent singular cardinals very good scale Forcing Antichain Vanishing levels Successor of Singular Cardinal Partition Relations Ascent Path Souslin Tree Erdos Cardinal SNR C-sequence Diamond-sharp approachability ideal Absoluteness Iterated forcing Commutative cancellative semigroups Sigma-Prikry reflection principles Forcing with side conditions Strongly compact cardinal GMA Almost Souslin O-space Distributive tree Filter reflection Sakurai's Bell inequality projective Boolean algebra Monotonically far Jonsson cardinal perfectly normal Countryman line Luzin set Subtle cardinal Hedetniemi's conjecture Prikry-type forcing Non-saturation Whitehead Problem club_AD Knaster Forcing Axioms ZFC construction Club Guessing Partition relations for trees Minimal Walks Open Access Closed coloring countably metacompact weak diamond L-space Was Ulam right? Chromatic number weak Kurepa tree full tree Hindman's Theorem Chang's conjecture Reduced Power incompactness Fast club Diamond for trees specializable Souslin tree stick Rock n' Roll Singular Density Slim tree Hereditarily Lindelöf space Large Cardinals regressive Souslin tree Knaster and friends Cardinal function Almost-disjoint family Cohen real diamond star square principles Commutative projection system Strongly Luzin set Parameterized proxy principle Intersection model Precaliber Sierpinski's onto mapping principle Ulam matrix Fat stationary set 54G20 Erdos-Hajnal graphs Generalized Clubs Ramsey theory over partitions Analytic sets Martin's Axiom P-Ideal Dichotomy Greatly Mahlo transformations free Souslin tree Dowker space indecomposable filter Rainbow sets Weakly compact cardinal Universal Sequences Well-behaved magma Aronszajn tree b-scale S-Space ccc weak square middle diamond strongly bounded groups Respecting tree
Category Archives: Publications
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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More notions of forcing add a square
Joint work with Yair Hayut and Zhixing You. Abstract. Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\omega_1}$. Here, we show that $\mathbb P$ may consistently be … Continue reading
Posted in Squares and Diamonds
Tagged full tree, Souslin Tree, square principles, super-Souslin tree
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40th summer conference on topology and its applications
I gave an invited talk at the General and Set-Theoretic Topology session of the 40th summer conference on topology and its applications, July 2026. Talk title: A tree-based perfectly normal space whose square is not countably metacompact. Abstract. The study … Continue reading
Posted in Invited Talks, Topology
Tagged Interval topology on trees
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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, Publications
Tagged Lipschitz reduction, Partition relations for trees
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Was Ulam right? III: Indecomposable ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Ulam’s measure problem. In contrast to our previous works, we shift our focus from measures stratified by their additivity, to measures stratified by their indecomposability. The breakthrough here is … Continue reading
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, and provides an … Continue reading
Posted in Compactness, Publications
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Subtle tree property, Vanishing levels
2 Comments
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
