A $Delta^0_2$ Theory of Regressive Isols

Journal of Symbolic Logic 39 (3):459-468 (1974)
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We examine the action of unary $\Delta^0_2$ functions on the regressive isols. A manageable theory is produced and we find that such a function maps $\Lambda_R$ into $\Lambda$ if and only if it is eventually $R\uparrow$ increasing and maps $\Lambda_R$ into $\Lambda_R$ if and only if it is eventually recursive increasing. Our paper concludes with a discussion of other methods for extending functions to $\Lambda_R$



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