Constants and classes of autoequivalent constructivizations. (Russian) Zbl 0709.03026
Computable invariants in the theory of algebraic systems, Collect. Sci. Works, Novosibirsk, 46-50 (1987).
[For the entire collection see Zbl 0687.00004.]
The author investigates how do constants affect autoequivalent constructivizations. Let \(\nu\) be a constructivization of the model \({\mathfrak A}\). The author denotes the class of autoequivalence of the constructivization \(\nu\) of the model \(<{\mathfrak A},a_ 1,...,a_ n>\) with distinguished constants by \([\nu,a_ 1,...,a_ n]\). The main result is: Theorem. There exists a constructivizable model \({\mathfrak A}\) such that for any constructivization \(\nu\) of it there are constructivizations \(\nu_ 0,\nu_ 1\in [\nu]\) such that for any \(a\in [{\mathfrak A}]\), \([\nu_ 0,a]\cap [\nu_ 1,a]=\emptyset\) and \([\nu]=[\nu_ 0,a]\cup [\nu_ 1,a]\). - The natural generalization for a finite number of classes is also obtained.
The author investigates how do constants affect autoequivalent constructivizations. Let \(\nu\) be a constructivization of the model \({\mathfrak A}\). The author denotes the class of autoequivalence of the constructivization \(\nu\) of the model \(<{\mathfrak A},a_ 1,...,a_ n>\) with distinguished constants by \([\nu,a_ 1,...,a_ n]\). The main result is: Theorem. There exists a constructivizable model \({\mathfrak A}\) such that for any constructivization \(\nu\) of it there are constructivizations \(\nu_ 0,\nu_ 1\in [\nu]\) such that for any \(a\in [{\mathfrak A}]\), \([\nu_ 0,a]\cap [\nu_ 1,a]=\emptyset\) and \([\nu]=[\nu_ 0,a]\cup [\nu_ 1,a]\). - The natural generalization for a finite number of classes is also obtained.
Reviewer: A.S.Morozov
MSC:
| 03C57 | Computable structure theory, computable model theory |
