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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
2 Comments
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
