Geodesic
Counterexamples in the Theory of ω-functions
Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 800-805

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Let ε stand for the set of nonnegative integers (numbers), V for the class of all subcollections of ε (sets), Λ for the set of isols, and ΛR for the set of regressive isols. A function, f, is a mapping from a subset of ε into ε and δf and ρf denote the domain and range of f respectively. The relation of inclusion is denoted by ⊂ and that of proper inclusion by ⊊. The sets α and β are recursively equivalent (written α ≃ β), if δf = α and ρf = β for some function f with a one-to-one partial recursive extension. 
Applebaum, C. H. Counterexamples in the Theory of ω-functions. Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 800-805. doi: 10.4153/CJM-1974-075-2
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[1] 1. Applebaum, C. H., ω-homomorphisms and ω-groups, J. Symbolic Logic 86 (1971), 55–65. Google Scholar

[2] 2. Applebaum, C. H. and J. C. E. Dekker, Partial recursive functions and ω-functions, J. Symbolic Logic 35 (1970), 559–568. Google Scholar

[3] 3. Barback, J., Two notes on regressive isols, Pacific J. Math. 16 (1966), 407–420. Google Scholar

[4] 4. Dekker, J. C. E., Infinite series of isols, Proceedings of the Symposium on Recursive Function Theory (Amer. Math. Soc, Providence, 1962), 77-96. Google Scholar

[5] 5. Dekker, J. C. E., The minimum of two regressive isols, Math. Z. 83 (1964), 345–366. Google Scholar

[6] 6. Dekker, J. C. E. and Myhill, J., Recursive equivalence types, Univ. of Calif. Publ. of Math. (N.S.) 3 (1960), 67–214. Google Scholar

[7] 7. Gonshor, H., The category of recursive functions, Fund. Math. 75 (1972), 87–94. Google Scholar

[8] 8. Hassett, M. J., Recursive equivalence types and groups, J. Symbolic Logic 34 (1969), 13–20. Google Scholar

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