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