Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2143

Preprint Number 2143

Previous Next Preprint server

2143. Mark Kamsma
Bilinear spaces over a fixed field are simple unstable

Submission date: 9 March 2022


We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we need different logical frameworks. First we take a category-theoretic approach, which requires very little set-up. We show that linear independence forms a simple unstable independence relation. With some more work we then show that we can also work in the framework of positive logic, which is much more powerful than the category-theoretic approach and much closer to the classical framework of full first-order logic. We fully characterise the existentially closed models of the arising positive theory. Using the independence relation from before we conclude that the theory is simple unstable, in the sense that dividing has local character but there are many distinct types.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2203.04844: pdf, ps.

Last updated: April 1 2022 15:18 Please send your corrections to: