FINITE UNDECIDABILITY IN NIP FIELDS-Reference-Cited by-同舟云学术

FINITE UNDECIDABILITY IN NIP FIELDS

Published:2023-10-04 Issue: Volume: Page:1-24
ISSN:0022-4812
Container-title:The Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

TYRRELL BRIAN

Abstract

Abstract A field K in a ring language

$\mathcal {L}$

is finitely undecidable if

$\mbox {Cons}(T)$

is undecidable for every nonempty finite

$T \subseteq {\mathtt{Th}}(K; \mathcal {L})$

. We extend a construction of Ziegler and (among other results) use a first-order classification of Anscombe and Jahnke to prove every NIP henselian nontrivially valued field is finitely undecidable. We conclude (assuming the NIP Fields Conjecture) that every NIP field is finitely undecidable. This work is drawn from the author’s PhD thesis [48, Chapter 3].

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

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