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Classical isol incomparability and ∞ · on manifold RET's

Part of: Computability and recursion theory

Published online by Cambridge University Press:  09 April 2009

Leon Harkleroad
Leon Harkleroad
Affiliation:
Department of Mathematics, Bellarmine College, Louisville, Kentucky, U.S.A.
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Abstract

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An infinite collection of indecomposable isols such that no isol is comparable to certain infinitary combinations of the others is constructed, extending a result of Dekker and Myhill. This collection is then used to investigate differences between the arithmetic of classical RET's and that of RET's on recursive manifolds, a difference relevant to the manifold equivalent of the Schröder-Bernstein Theorem.

MSC classification

Secondary: 03D50: Recursive equivalence types of sets and structures, isols
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 99 - 114
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Dekker, J. C. E. and Myhill, John, Recursive equivalence types, (University of California Publications in Mathematics, New Series, Vol. 3, No. 3, 1960, pp. 67–214).Google Scholar
[2]Harkleroad, L., ‘Recursive equivalence types on recursive manifolds’, Notre Dame J. Formal Logic 20 (1979), 1–31.CrossRefGoogle Scholar
[3]Harkleroad, L., ‘Iterated images on manifolds’, Noire Dame J. Formal Logic, to appear.Google Scholar