Author:
Chisholm J.,Knight J. F.,Miller S.
Abstract
AbstractHere we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over ℚ, and ZS is the class of models of Th(ℤ, S). Similarly, we show that there is no computable embedding of ACF into ZS, where ACF is the class of algebraically closed fields of characteristic 0.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. Knight J. F. , A result on the degree structures associated with effective embeddings, preprint.
2. Hjorth G. and Thomas S. , The classification problem for p-local torsion-free Abelian groups of rank two, preprint.
3. The isomorphism relation on countable torsion free abelian groups
4. The completeness of the isomorphism relation for countable Boolean algebras
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献