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
Effective Ringed Spaces And Turing Degrees Of Isomorphism Types
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
The Turing degree spectrum of a countable structure A is the set of all Turing degrees of isomorphic copies of A. The Turing degree of the isomorphism type of A is the least degree in this spectrum, if there is a least degree. Frequently one can prove that, for a given class K of structures (e.g., the class of fields), for any Turing degree d there is an element of K whose isomorphism type has degree d. Frequently this result is established by finding that K has certain combinatorial properties. Here we show that this universality property holds for various classes of ringed spaces: unions of subvarieties of a fixed variety, unions of arbitrary ringed spaces, and schemes.
No Notes/Supplements UploadedEffective Ringed Spaces And Turing Degrees Of Isomorphism Types
| H.264 Video | 25183_28681_8507_Effective_Ringed_Spaces_and_Turing_Degrees_of_Isomorphism_Types.mp4 |