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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
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Stevo Todorcevic Poset Cardinal Invariants Sakurai's Bell inequality approachability ideal Foundations incompactness Singular cardinals combinatorics Minimal Walks Aronszajn tree Slim tree very good scale Martin's Axiom Almost countably chromatic Prevalent singular cardinals Partition Relations xbox Universal Sequences Prikry-type forcing stationary hitting Forcing PFA(S)[S] Forcing Axioms Hereditarily Lindelöf space Singular coﬁnality Parameterized proxy principle Fodor-type reflection Cohen real Uniformization 05A17 05D10 Successor of Singular Cardinal Antichain Chang's conjecture square Almost Souslin Constructible Universe Erdos-Hajnal graphs weak square Fast club Ostaszewski square Club Guessing ccc Square-Brackets Partition Relations Generalized Clubs middle diamond Rock n' Roll Kurepa Hypothesis Knaster 20M14 Large Cardinals Cardinal function 11P99 Whitehead Problem Fat stationary set Singular Cofinality Successor of Regular Cardinal Rado's conjecture coloring number Souslin Tree Shelah's Strong Hypothesis diamond star Singular Density Hedetniemi's conjecture Almost-disjoint famiy weak diamond Mandelbrot set projective Boolean algebra stationary reflection Selective Ultrafilter Small forcing S-Space Ascent Path reflection principles OCA Non-saturation Microscopic Approach sap L-space b-scale Rainbow sets Erdos Cardinal HOD P-Ideal Dichotomy Absoluteness PFA Dushnik-Miller Weakly compact cardinal Coherent tree polarized partition relation free Boolean algebra Commutative cancellative semigroups Chromatic number Reduced Power Axiom R tensor product graph Diamond Jonsson cardinal Hindman's Theorem square principles

# Tag Archives: 05A17

## 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