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free Souslin tree Reflecting stationary set Singular cofinality PFA(S)[S] full tree Countryman line Prikry-type forcing Generalized descriptive set theory middle diamond Ramsey theory over partitions Rado's conjecture Singular Density Chang's conjecture Ascent Path Rock n' Roll Slim tree Dowker space Almost Souslin Ineffable cardinal square Absoluteness Intersection model Whitehead Problem Parameterized proxy principle higher Baire space Successor of Singular Cardinal tensor product graph Antichain Hedetniemi's conjecture L-space Chromatic number Hindman's Theorem Open Access Microscopic Approach Weakly compact cardinal Analytic sets PFA Local Club Condensation. sap very good scale nonmeager set ccc Uniformization S-Space Constructible Universe projective Boolean algebra Jonsson cardinal Diamond-sharp Commutative projection system Kurepa Hypothesis Fat stationary set Fast club weak square reflection principles Strong coloring Respecting tree Non-saturation polarized partition relation transformations Ulam matrix incompactness Selective Ultrafilter Rainbow sets Small forcing Diamond for trees Luzin set positive partition relation AIM forcing club_AD weak Kurepa tree Axiom R stick Cardinal Invariants Amenable C-sequence free Boolean algebra Iterated forcing Cohen real Strongly Luzin set Sierpinski's onto mapping principle Generalized Clubs Subtle tree property HOD O-space Nonspecial tree Sigma-Prikry C-sequence OCA Ostaszewski square Dushnik-Miller SNR stationary hitting Club Guessing Square-Brackets Partition Relations Fodor-type reflection strongly bounded groups square principles Successor of Regular Cardinal Subadditive Sakurai's Bell inequality Hereditarily Lindelöf space approachability ideal 54G20 Uniformly homogeneous Foundations Subtle cardinal Mandelbrot set Poset stationary reflection weak diamond Closed coloring diamond star Lipschitz reduction Diamond xbox Prevalent singular cardinals Commutative cancellative semigroups Forcing Axioms Almost countably chromatic Greatly Mahlo Minimal Walks specializable Souslin tree Erdos Cardinal Knaster Partition Relations Erdos-Hajnal graphs Subnormal ideal Well-behaved magma Souslin Tree Coherent tree indecomposable ultrafilter Almost-disjoint family unbounded function Universal Sequences Shelah's Strong Hypothesis Aronszajn tree Large Cardinals Filter reflection Singular cardinals combinatorics Vanishing levels Postprocessing function regressive Souslin tree ZFC construction Knaster and friends b-scale Reduced Power GMA Distributive tree Was Ulam right? Uniformly coherent Precaliber Forcing Martin's Axiom countably metacompact Strongly compact cardinal P-Ideal Dichotomy Cardinal function super-Souslin tree coloring number
Blog Archives
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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Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the
A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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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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