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54G20 Singular cofinality stationary reflection very good scale Strongly Luzin set Distributive tree Absoluteness Forcing Axioms PFA(S)[S] Well-behaved magma Uniformly homogeneous middle diamond O-space Vanishing levels Chromatic number diamond star Non-saturation Ostaszewski square Universal Sequences weak diamond free Souslin tree Subnormal ideal Parameterized proxy principle approachability ideal Fast club Dushnik-Miller Partition Relations nonmeager set strongly bounded groups Antichain Jonsson cardinal Cohen real Square-Brackets Partition Relations Uniformization Forcing Mandelbrot set Diamond for trees Reflecting stationary set Hindman's Theorem Nonspecial tree Weakly compact cardinal OCA Souslin Tree unbounded function Reduced Power polarized partition relation SNR Closed coloring Whitehead Problem Rock n' Roll Greatly Mahlo Sierpinski's onto mapping principle Fat stationary set club_AD Almost countably chromatic Poset free Boolean algebra Kurepa Hypothesis Almost Souslin Analytic sets tensor product graph incompactness b-scale stationary hitting Successor of Singular Cardinal Strong coloring Local Club Condensation. Selective Ultrafilter weak Kurepa tree coloring number Hedetniemi's conjecture Knaster specializable Souslin tree regressive Souslin tree Prikry-type forcing higher Baire space full tree Generalized descriptive set theory AIM forcing Ineffable cardinal xbox Commutative cancellative semigroups P-Ideal Dichotomy Shelah's Strong Hypothesis Small forcing Hereditarily Lindelöf space Almost-disjoint family S-Space reflection principles Successor of Regular Cardinal L-space ZFC construction Large Cardinals Chang's conjecture Cardinal function Rainbow sets Slim tree Uniformly coherent Minimal Walks weak square sap indecomposable ultrafilter Fodor-type reflection Sakurai's Bell inequality C-sequence super-Souslin tree Coherent tree Diamond-sharp Cardinal Invariants Foundations Singular cardinals combinatorics Diamond Amenable C-sequence Erdos-Hajnal graphs Dowker space Erdos Cardinal countably metacompact HOD square Knaster and friends Aronszajn tree Postprocessing function Was Ulam right Precaliber Iterated forcing Ramsey theory over partitions positive partition relation transformations Subtle tree property stick Ascent Path Prevalent singular cardinals GMA Luzin set Axiom R Filter reflection square principles Subtle cardinal Constructible Universe Subadditive PFA Rado's conjecture Sigma-Prikry Ulam matrix Lipschitz reduction projective Boolean algebra Singular Density Generalized Clubs Microscopic Approach ccc Club Guessing Martin's Axiom Open Access
Tag Archives: Fodor-type reflection
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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Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading