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Absoluteness Forcing Knaster O-space Axiom R Minimal Walks Shelah's Strong Hypothesis tensor product graph Local Club Condensation. Sigma-Prikry Subadditive unbounded function Club Guessing Almost countably chromatic Ulam matrix Prikry-type forcing very good scale Constructible Universe Fast club polarized partition relation reflection principles Erdos-Hajnal graphs Generalized Clubs ccc Fodor-type reflection PFA(S)[S] Cohen real Uniformization Martin's Axiom P-Ideal Dichotomy Iterated forcing indecomposable ultrafilter Forcing Axioms Analytic sets Amenable C-sequence Closed coloring Kurepa Hypothesis xbox Luzin set strongly bounded groups middle diamond ZFC construction Filter reflection Open Access Chang's conjecture Almost-disjoint family Strongly Luzin set Erdos Cardinal 54G20 stationary reflection Diamond-sharp Antichain Ramsey theory over partitions free Souslin tree Greatly Mahlo Vanishing levels Cardinal Invariants Cardinal function Square-Brackets Partition Relations Partition Relations Foundations Fat stationary set Rock n' Roll Large Cardinals square Diamond Reflecting stationary set Prevalent singular cardinals Generalized descriptive set theory Precaliber Ascent Path Rado's conjecture Uniformly homogeneous stick weak Kurepa tree Well-behaved magma nonmeager set transformations Singular Density Aronszajn tree Weakly compact cardinal AIM forcing higher Baire space Non-saturation Hindman's Theorem GMA positive partition relation L-space weak diamond Coherent tree super-Souslin tree Hedetniemi's conjecture Knaster and friends coloring number specializable Souslin tree Nonspecial tree square principles Ineffable cardinal sap b-scale Sakurai's Bell inequality free Boolean algebra Almost Souslin Chromatic number weak square Singular cofinality Selective Ultrafilter Diamond for trees Dushnik-Miller Rainbow sets Successor of Regular Cardinal incompactness Was Ulam right stationary hitting Hereditarily Lindelöf space Poset Uniformly coherent regressive Souslin tree full tree Jonsson cardinal club_AD projective Boolean algebra HOD diamond star Singular cardinals combinatorics OCA PFA Slim tree Universal Sequences Strong coloring Small forcing Sierpinski's onto mapping principle Distributive tree countably metacompact Subtle cardinal Whitehead Problem C-sequence Subnormal ideal Parameterized proxy principle Subtle tree property S-Space Commutative cancellative semigroups Souslin Tree Dowker space Postprocessing function SNR approachability ideal Ostaszewski square Reduced Power Successor of Singular Cardinal Microscopic Approach Lipschitz reduction Mandelbrot set
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Partitioning the club guessing
In a recent paper, I am making use of the following fact. Theorem (Shelah, 1997). Suppose that $\kappa$ is an accessible cardinal (i.e., there exists a cardinal $\theta<\kappa$ such that $2^\theta\ge\kappa)$. Then there exists a sequence $\langle g_\delta:C_\delta\rightarrow\omega\mid \delta\in E^{\kappa^+}_\kappa\rangle$ … Continue reading
