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Partition Relations Absoluteness Ramsey theory over partitions Fodor-type reflection stationary hitting Large Cardinals Jonsson cardinal Cohen real Subnormal ideal stick Kurepa Hypothesis Respecting tree GMA Subadditive polarized partition relation Erdos Cardinal Forcing Axioms weak Kurepa tree Non-saturation Slim tree Diamond Ineffable cardinal Commutative cancellative semigroups Almost Souslin Minimal Walks Rainbow sets Strongly compact cardinal Amenable C-sequence C-sequence Axiom R Poset b-scale Hindman's Theorem Rado's conjecture Distributive tree Dushnik-Miller Uniformly coherent Ascent Path Ostaszewski square Square-Brackets Partition Relations middle diamond sap Uniformization Sigma-Prikry P-Ideal Dichotomy Reduced Power projective Boolean algebra Was Ulam right? Knaster and friends Microscopic Approach tensor product graph Martin's Axiom Well-behaved magma Erdos-Hajnal graphs free Souslin tree incompactness approachability ideal square principles club_AD Club Guessing Dowker space Nonspecial tree transformations xbox PFA Strongly Luzin set Constructible Universe Shelah's Strong Hypothesis Postprocessing function Commutative projection system Analytic sets Fast club O-space Universal Sequences Whitehead Problem Antichain Closed coloring Hedetniemi's conjecture Rock n' Roll positive partition relation stationary reflection Diamond-sharp diamond star Chromatic number indecomposable ultrafilter Local Club Condensation. ZFC construction countably metacompact Prevalent singular cardinals Singular cofinality Singular Density unbounded function Souslin Tree Almost countably chromatic Almost-disjoint family Hereditarily Lindelöf space Diamond for trees Successor of Singular Cardinal Small forcing Cardinal Invariants Subtle tree property Chang's conjecture very good scale Sakurai's Bell inequality Parameterized proxy principle Foundations Iterated forcing free Boolean algebra OCA full tree nonmeager set Prikry-type forcing Selective Ultrafilter AIM forcing Fat stationary set Vanishing levels HOD square specializable Souslin tree ccc Coherent tree Intersection model Reflecting stationary set strongly bounded groups Cardinal function Singular cardinals combinatorics Lipschitz reduction S-Space regressive Souslin tree Forcing SNR higher Baire space Countryman line Precaliber weak square Generalized descriptive set theory coloring number Mandelbrot set Open Access reflection principles L-space PFA(S)[S] Ulam matrix Aronszajn tree super-Souslin tree Subtle cardinal Strong coloring Filter reflection 54G20 Luzin set Greatly Mahlo Sierpinski's onto mapping principle Weakly compact cardinal Uniformly homogeneous Generalized Clubs weak diamond Successor of Regular Cardinal Knaster
Tag Archives: Iterated forcing
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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Sigma-Prikry forcing III: Down to Aleph_omega
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … Continue reading
Sigma-Prikry forcing II: Iteration Scheme
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. In Part I of this series, we introduced a class of notions of forcing which we call
The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … Continue reading
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
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The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let
