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