Krull dimension of types in a class of first-order theories
Logic
2009-06-01 v2
Abstract
We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula--plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.
Keywords
Cite
@article{arxiv.0812.3489,
title = {Krull dimension of types in a class of first-order theories},
author = {Domenico Zambella},
journal= {arXiv preprint arXiv:0812.3489},
year = {2009}
}
Comments
Major revision, new title