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- A strong form of König’s lemma October 21, 2017
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### Keywords

Axiom R Hindman's Theorem Generalized Clubs Small forcing 11P99 Rado's conjecture coloring number diamond star Diamond tensor product graph Ostaszewski square Sakurai's Bell inequality Partition Relations Fodor-type reflection Parameterized proxy principle weak diamond Forcing PFA(S)[S] PFA Nonspecial tree S-Space P-Ideal Dichotomy Postprocessing function Forcing Axioms Rock n' Roll xbox Fast club Cardinal function Ascent Path square Martin's Axiom Knaster Reduced Power Universal Sequences free Boolean algebra Singular coﬁnality Slim tree Selective Ultrafilter Large Cardinals Rainbow sets Chang's conjecture sap Coherent tree Absoluteness Mandelbrot set incompactness Non-saturation Singular cardinals combinatorics Stevo Todorcevic OCA Successor of Regular Cardinal projective Boolean algebra stationary reflection Successor of Singular Cardinal Dushnik-Miller Hereditarily Lindelöf space Prevalent singular cardinals Hedetniemi's conjecture Antichain weak square Square-Brackets Partition Relations 20M14 Singular Density approachability ideal super-Souslin tree Shelah's Strong Hypothesis Club Guessing Weakly compact cardinal Cohen real Whitehead Problem Prikry-type forcing 05A17 Erdos Cardinal Almost-disjoint famiy Kurepa Hypothesis Cardinal Invariants Constructible Universe Souslin Tree Aronszajn tree Uniformization square principles b-scale Chromatic number Minimal Walks Luzin set Distributive tree Almost countably chromatic middle diamond Uniformly coherent Almost Souslin Fat stationary set Foundations Jonsson cardinal reflection principles Microscopic Approach Poset polarized partition relation L-space ccc very good scale Commutative cancellative semigroups Erdos-Hajnal graphs stationary hitting HOD

# Tag Archives: 11P99

## Strong failures of higher analogs of Hindman’s Theorem

Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading