Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T16:23:31.576Z Has data issue: false hasContentIssue false

Classical isol incomparability and ∞ · on manifold RET's

Published online by Cambridge University Press:  09 April 2009

Leon Harkleroad
Affiliation:
Department of Mathematics, Bellarmine College, Louisville, Kentucky, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
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. 67214).Google Scholar
[2]Harkleroad, L., ‘Recursive equivalence types on recursive manifolds’, Notre Dame J. Formal Logic 20 (1979), 131.CrossRefGoogle Scholar
[3]Harkleroad, L., ‘Iterated images on manifolds’, Noire Dame J. Formal Logic, to appear.Google Scholar