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54G20 L-space GMA Dowker space Knaster and friends Cardinal Invariants Coherent tree square principles middle diamond Souslin Tree Subnormal ideal AIM forcing Minimal Walks Square-Brackets Partition Relations Singular Density Sierpinski's onto mapping principle O-space weak square Kurepa Hypothesis Intersection model Jonsson cardinal Diamond-sharp sap Forcing HOD indecomposable ultrafilter Shelah's Strong Hypothesis Mandelbrot set Commutative cancellative semigroups Analytic sets approachability ideal polarized partition relation Ulam matrix Ramsey theory over partitions Diamond club_AD Sakurai's Bell inequality Luzin set Small forcing Fast club Forcing Axioms Prevalent singular cardinals Hereditarily Lindelöf space projective Boolean algebra countably metacompact weak Kurepa tree S-Space Chang's conjecture Rainbow sets Uniformization ccc Strongly compact cardinal Axiom R Open Access incompactness higher Baire space Ascent Path Singular cardinals combinatorics Was Ulam right? Subadditive Dushnik-Miller Successor of Singular Cardinal Martin's Axiom Filter reflection Almost countably chromatic Uniformly homogeneous Sigma-Prikry Poset Knaster ZFC construction PFA(S)[S] Universal Sequences transformations Reduced Power xbox Reflecting stationary set Aronszajn tree PFA stationary hitting Lipschitz reduction free Boolean algebra square strongly bounded groups very good scale free Souslin tree coloring number Closed coloring stick Ostaszewski square P-Ideal Dichotomy Greatly Mahlo Chromatic number diamond star Countryman line Well-behaved magma reflection principles Diamond for trees Fodor-type reflection Commutative projection system C-sequence Hindman's Theorem Subtle tree property Constructible Universe Prikry-type forcing Iterated forcing Club Guessing Uniformly coherent Fat stationary set Local Club Condensation. Selective Ultrafilter Whitehead Problem Respecting tree full tree Antichain Erdos-Hajnal graphs Amenable C-sequence Rock n' Roll Precaliber Absoluteness Almost Souslin nonmeager set Foundations Subtle cardinal Ineffable cardinal Non-saturation Generalized Clubs Cardinal function Strongly Luzin set Microscopic Approach SNR Almost-disjoint family Rado's conjecture specializable Souslin tree weak diamond Nonspecial tree unbounded function Postprocessing function Parameterized proxy principle Slim tree OCA b-scale positive partition relation Cohen real super-Souslin tree Hedetniemi's conjecture regressive Souslin tree Erdos Cardinal tensor product graph Distributive tree Strong coloring Successor of Regular Cardinal Weakly compact cardinal Generalized descriptive set theory Singular cofinality Large Cardinals Partition Relations stationary reflection Vanishing levels
Category Archives: Publications
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
Posted in Compactness, Preprints
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Vanishing levels
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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
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable ultrafilter, Intersection model, Strongly compact cardinal
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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 only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Posted in Preprints, Squares and Diamonds
Tagged Diamond, Diamond for trees, Iterated forcing, Kurepa Hypothesis, weak Kurepa tree
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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
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
Posted in Compactness, Preprints
Tagged Forcing Axioms, indecomposable ultrafilter, Subadditive, unbounded function
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May the successor of a singular cardinal be Jonsson?
Abstract: We collect necessary conditions for the successor of a singular cardinal to be Jónsson.
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal
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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
