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Generalized descriptive set theory Postprocessing function polarized partition relation S-Space positive partition relation PFA C-sequence Souslin Tree Whitehead Problem Selective Ultrafilter HOD Club Guessing Nonspecial tree Knaster Minimal Walks Hedetniemi's conjecture Erdos Cardinal Commutative cancellative semigroups Successor of Singular Cardinal Diamond Diamond-sharp stationary reflection Filter reflection Chromatic number Strongly Luzin set Non-saturation Sierpinski's onto mapping principle Forcing Mandelbrot set Countryman line Ostaszewski square countably metacompact Ascent Path approachability ideal Fodor-type reflection Luzin set Kurepa Hypothesis nonmeager set Respecting tree very good scale stick Knaster and friends Small forcing Fast club Weakly compact cardinal Prevalent singular cardinals club_AD super-Souslin tree Cardinal function Subadditive Precaliber full tree Almost-disjoint family Prikry-type forcing Subnormal ideal Aronszajn tree Strongly compact cardinal square principles Hereditarily Lindelöf space Iterated forcing Square-Brackets Partition Relations Partition Relations Rado's conjecture Sigma-Prikry unbounded function Fat stationary set indecomposable ultrafilter b-scale Foundations Singular cardinals combinatorics Slim tree Rainbow sets Reduced Power strongly bounded groups Ulam matrix Subtle cardinal Closed coloring weak square diamond star Hindman's Theorem 54G20 Strong coloring Rock n' Roll transformations incompactness stationary hitting Ramsey theory over partitions Forcing Axioms Intersection model Large Cardinals reflection principles Subtle tree property Almost countably chromatic Absoluteness higher Baire space xbox Shelah's Strong Hypothesis weak Kurepa tree free Souslin tree PFA(S)[S] Erdos-Hajnal graphs tensor product graph Reflecting stationary set Was Ulam right? coloring number free Boolean algebra OCA GMA ccc sap Singular cofinality Cohen real Greatly Mahlo Uniformization regressive Souslin tree P-Ideal Dichotomy Singular Density Uniformly coherent Coherent tree Microscopic Approach Martin's Axiom L-space Constructible Universe Distributive tree AIM forcing Almost Souslin O-space ZFC construction Universal Sequences projective Boolean algebra Amenable C-sequence Generalized Clubs Open Access Vanishing levels Sakurai's Bell inequality Analytic sets Well-behaved magma Commutative projection system Parameterized proxy principle Dushnik-Miller weak diamond SNR Lipschitz reduction Diamond for trees specializable Souslin tree Jonsson cardinal Uniformly homogeneous Antichain Successor of Regular Cardinal Chang's conjecture Dowker space Ineffable cardinal Poset Cardinal Invariants Local Club Condensation. square Axiom R middle diamond
Category Archives: Preprints
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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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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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
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Prikry-type forcing, ZFC construction
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