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  1. Finite Undecidability in Nip Fields.Brian Tyrrell - forthcoming - Journal of Symbolic Logic:1-24.
    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].
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  • Finite undecidability in PAC and PRC fields.Brian Tyrrell - 2024 - Annals of Pure and Applied Logic 175 (10):103465.
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