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Construction of models for algebraically generalized recursive function theory

Published online by Cambridge University Press:  12 March 2014

H. R. Strong
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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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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 3 , September 1970, pp. 401 - 409
Copyright
Copyright © Association for Symbolic Logic 1971

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References

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