Recursive categoricity and recursive stability

Crossley, John N.; Manaster, Alfred B.; Moses, Michael

doi:10.1016/0168-0072(86)90070-9

Cited by 8 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Various aspects of this notion have been studied by many authors [6,[13][14][15]. In some cases, under additional assumptions, a model proved to be autostable if and only if a relevant algebraic condition (finiteness of a certain definable subset or, in a wider setting, the existence of an appropriate computable Scott family) is satisfied.…”

Section: Effective Choice Of Reducing Functions For Autostable Modelsmentioning

confidence: 98%

Effective choice for relations and reducibilities in classes of constructive and positive models

Ventsov¹

1992

Algebr Logic

View full text Add to dashboard Cite

The study of effective choice problems has been initiated in [I, 2]. The very notion of effective choice for a class of constructive objects can be identified with effective construction of relevant objects.The problems in question admit distinct variations in classes of constructive and positive models, and in most cases, are amenable to transparent formalization. Thus, in studies dealing with the autostability of models and intrinsically recursive enumerability of relations on them, these notions can be specified naturally with regard for the possibility of constructing effectively a reducing function for ~ the two given constructivizations and, correspondingly, an enumeration procedure for the given constructivization and relation.Another important aspect in the study of effective choice problems arises from the fact (see [3]) that without effective choice, the notions of autostability and intrinsically recursive enumerability in classes of constructive models cannot be described naturally in terms of the algebraic properties of models.In this paper we adopt the notation and follow the definitions of [4][5][6][7].Let ,~![ be a countable model in a fixed finite signature _~, containing a predicate symbol for equality.By ~L~} we denote the set of all relations on L~ (subsets of an appropriate Cartesian power I~ v] ) that are stable under automorphisms of L~,~.

show abstract

Section: Effective Choice Of Reducing Functions For Autostable Modelsmentioning

confidence: 98%