Brian Tyrrell

collaborators

4 papers

math.LO2022

Finite Undecidability in Fields II: PAC, PRC and PpC Fields

Brian Tyrrell

A field $K$ in a ring language $L$ is finitely undecidable if $\mbox{Cons}(Σ)$ is undecidable for every nonempty finite $Σ\subseteq \mbox{Th}(K; \mathcal{L})$. We adapt a…

math.LO2022

Finite Undecidability in Fields I: NIP Fields

Brian Tyrrell

A field $K$ in a ring language $L$ is finitely undecidable if $\mbox{Cons}(Σ)$ is undecidable for every nonempty finite $Σ\subseteq \mbox{Th}(K; \mathcal{L})$. We extend…

math.LO2019

A Note on Hilbert's "Geometric" Tenth Problem

Brian Tyrrell

This paper explores undecidability in theories of positive characteristic function fields in the "geometric" language of rings $L_{F} = {0, 1, +, \cdot, F}$ , with a unary…

math.LO2019

A New Universal Definition of $F_{q} [t]$ in $F_{q} (t)$

Brian Tyrrell

This paper gives a universal definition of $F_{q} [t]$ in $F_{q} (t)$ using 89 quantifiers, more direct than those that exist in the current literature. The language…

Finite Undecidability in Fields II: PAC, PRC and PpC Fields

Finite Undecidability in Fields I: NIP Fields

A Note on Hilbert's "Geometric" Tenth Problem

A New Universal Definition of Fq​[t] in Fq​(t)

A New Universal Definition of $F_{q} [t]$ in $F_{q} (t)$