Search

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].

The arithmetic is interpreted in all the groups of Richard Thompson and Graham Higman, as well as in other groups of piecewise affine permutations of an interval which generalize the groups of Thompson and Higman. In particular, the elementary theories of all these groups are undecidable. Moreover, Thompson's group F and some of its generalizations interpret the arithmetic without parameters.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

FINITE UNDECIDABILITY IN NIP FIELDS

Interprétation de l'arithmétique dans certains groupes de permutations affines par morceaux d'un intervalle

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

FINITE UNDECIDABILITY IN NIP FIELDS

Interprétation de l'arithmétique dans certains groupes de permutations affines par morceaux d'un intervalle