“Weak yet strong” restrictions of Hindman’s Finite Sums Theorem

Author:

Carlucci Lorenzo

Abstract

We present a natural restriction of Hindman’s Finite Sums Theorem that admits a simple combinatorial proof (one that does not also prove the full Finite Sums Theorem) and low computability-theoretic and proof-theoretic upper bounds, yet implies the existence of the Turing Jump, thus realizing the only known lower bound for the full Finite Sums Theorem. This is the first example of this kind. In fact we isolate a rich family of similar restrictions of Hindman’s Theorem with analogous properties.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference23 articles.

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