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Construction of Models for Algebraically Generalized Recursive Function Theory

H. R. Strong
The Journal of Symbolic Logic
Vol. 35, No. 3 (Sep., 1970), pp. 401-409
DOI: 10.2307/2270697
Stable URL: http://www.jstor.org/stable/2270697
Page Count: 9
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Construction of Models for Algebraically Generalized Recursive Function Theory
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Abstract

The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each countable Boolean algebra R of subsets of a countable set which contains the finite subsets, a model is constructed with R as its family of computable sets.

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