Homogeneous models and almost decidability

Journal of the Australian Mathematical Society

Terry Millar¹ 

关键词: 03 C 57;   

DOI  :  10.1017/S1446788700030834

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Countable homogeneous models are ‘simple’ objects from a model theoretic point of view. From a recursion theoretic point of view they can be complex. For instance the elementary theory of such a model might be undecidable, or the set of complete types might be recursively complex. Unfortunately even if neither of these conditions holds, such a model still can be undecidable. This paper investigates countable homogeneous models with respect to a weaker notion of decidability called almost decidable. It is shown that for theories that have only countably many type spectra, any countable homogeneous model of such a theory that has a Σ2 type spectrum is almost decidable.

【 授权许可】

Unknown