A universal first-order formula for the ring of integers inside a number field
Event details
| Date | 09.08.2012 |
| Hour | 11:15 › 12:30 |
| Speaker | Jennifer Park |
| Location | |
| Category | Conferences - Seminars |
Hilbert's tenth problem over Q (or, any number field K) asks the following: given a polynomial in several variables with coefficients in Q (resp. K), is there a
general algorithm that decides whether this polynomial has a solution in Q (resp. K)? Unlike the classical Hilbert's tenth problem over Z, this problem is still open.
To reduce this problem to the classical problem, we need a definition of Z in Q (resp. ring of integers in K) using only an existential quantifier. This problem is
still open. I will present a definition of the ring of integers in a number field, which uses only one universal quantifier, which is, in a sense, the simplest logical
description that we can hope for. This is a generalization of Koenigsmann's work, which defines Z in Q using one universal quantifier.
general algorithm that decides whether this polynomial has a solution in Q (resp. K)? Unlike the classical Hilbert's tenth problem over Z, this problem is still open.
To reduce this problem to the classical problem, we need a definition of Z in Q (resp. ring of integers in K) using only an existential quantifier. This problem is
still open. I will present a definition of the ring of integers in a number field, which uses only one universal quantifier, which is, in a sense, the simplest logical
description that we can hope for. This is a generalization of Koenigsmann's work, which defines Z in Q using one universal quantifier.
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Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii