Logic Seminar - Victor Lisinski (Oxford)
| Dates: | 27 April 2022 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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Title: Decidability of equal characteristic tame Hahn fields in the language L_t
Abstract: The model theory of tame fields in the language of valued fields has been extensively studied by Kuhlmann. In particular, the theory of an equal characteristic tame field in this language is given by the theory of the residue field and the theory of the value group. Building on Kuhlmann's results, we give an AKE-principle for tame valued fields of equal characteristic in L_t, the language of valued fields with a distinguished constant symbol t. Furthermore, we use this principle together with Kedlaya's work on the connection between generalised power series and finite automata to show that a tame Hahn field of equal characteristic is decidable in L_t if it has decidable residue field and decidable value group. In particular, we obtain decidability of F_p((t^Q )) in L_t. Finally, we will see how approximation methods used in this work reveal a condition on algebraicity for generalised power series in terms of the order type of the support.
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