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