Seminar
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| Location: | SLMath: Online/Virtual |
Hilbert’s Tenth Problem was the only decision problem among his twenty-three problems. Precise mathematical theory of (in)computability and its interaction with number theory led to the negative solution of the problem. The seminar will focus on modern topics on computability-theoretic phenomena in number-theoretic and other algebraic and model-theoretic structures.
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Milliken's Tree Theorem And Computability Theory
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Abstract:
Milliken's tree theorem is a powerful combinatorial result that generalizes Ramsey's theorem and many other familiar partition results. I will present recent work on the effective and proof-theoretic strength of this theorem, which was originally motivated by a question of Dobrinen. The main result is a complete characterization of Milliken's tree theorem in terms of reverse mathematics and the usual computability-theoretic hierarchies, along with several applications to other combinatorial problems. Key to this is a new inductive proof of Milliken's tree theorem, employing an effective version of the Halpern-Lauchli theorem. This is joint work with Angles d'Auriac, Cholak, Monin, and Patey.
No Notes/Supplements UploadedMilliken's Tree Theorem And Computability Theory
| H.264 Video | 25193_28691_8552_Milliken's_Tree_Theorem_and_Computability_Theory.mp4 |