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Forcing sap square Selective Ultrafilter Knaster and friends club_AD Successor of Singular Cardinal Open Access Hedetniemi's conjecture AIM forcing PFA(S)[S] Diamond-sharp strongly bounded groups tensor product graph Subtle cardinal Vanishing levels Diamond weak diamond countably metacompact Ostaszewski square Large Cardinals incompactness middle diamond stationary hitting OCA Local Club Condensation. Generalized descriptive set theory indecomposable ultrafilter Distributive tree Chromatic number Respecting tree Lipschitz reduction very good scale Chang's conjecture Small forcing nonmeager set Mandelbrot set weak Kurepa tree Ineffable cardinal Fodor-type reflection Subtle tree property Universal Sequences Strongly compact cardinal projective Boolean algebra Subadditive Fat stationary set Fast club Prevalent singular cardinals Iterated forcing C-sequence Reduced Power Uniformly homogeneous Non-saturation Countryman line Postprocessing function Axiom R regressive Souslin tree Uniformization Kurepa Hypothesis reflection principles Antichain polarized partition relation Poset Commutative projection system stationary reflection transformations Sierpinski's onto mapping principle GMA Strong coloring P-Ideal Dichotomy Absoluteness Rock n' Roll Minimal Walks Diamond for trees b-scale HOD Subnormal ideal Uniformly coherent Filter reflection Foundations Ascent Path Strongly Luzin set Sigma-Prikry Precaliber Parameterized proxy principle Coherent tree Aronszajn tree Almost Souslin square principles Shelah's Strong Hypothesis full tree Knaster Erdos-Hajnal graphs Singular cardinals combinatorics Dushnik-Miller Generalized Clubs Erdos Cardinal Singular cofinality positive partition relation Almost countably chromatic Almost-disjoint family unbounded function Hereditarily Lindelöf space Jonsson cardinal Constructible Universe Martin's Axiom Nonspecial tree O-space Forcing Axioms Analytic sets Sakurai's Bell inequality Commutative cancellative semigroups Ramsey theory over partitions Well-behaved magma Was Ulam right Souslin Tree Slim tree 54G20 specializable Souslin tree Microscopic Approach Club Guessing Amenable C-sequence Square-Brackets Partition Relations Singular Density S-Space Successor of Regular Cardinal free Boolean algebra xbox approachability ideal Whitehead Problem Closed coloring Rado's conjecture Greatly Mahlo weak square Cardinal function stick free Souslin tree PFA Weakly compact cardinal Intersection model Dowker space Hindman's Theorem Cardinal Invariants Prikry-type forcing diamond star coloring number Reflecting stationary set Cohen real SNR Rainbow sets ZFC construction Luzin set ccc Partition Relations higher Baire space L-space Ulam matrix super-Souslin tree
Category Archives: Publications
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. It is proved that if there is an $\aleph_2$-Aronszajn line, then there is one that does not contain an $\aleph_2$-Countryman line. This solves a problem of Moore and stands in a sharp contrast with … 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 $\kappa$-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
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 $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
