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Recursive Embeddings of Partial Orderings

Published online by Cambridge University Press:  20 November 2018

K. R. Apt
K. R. Apt*
Affiliation:
Mathematical Centre, 2e Boerhaavestraat 49, Amsterdam 1005, The Netherlands
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Abstract

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Let be a countable atomless Boolean algebra and let X be a countable partial ordering. We prove that there exists an embedding of X into which is recursive in X, and which destroys all suprema and infima of X which can be destroyed. We show that the above theorem is false when we try to preserve all suprema and infima of X instead of destroying them.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 349 - 359
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Abian, A., Categoricity of denumerable atomless Boolean rings, Studia Logica (1972), 63–68.Google Scholar
2. van Emde Boas, P., Mostowski's universal set-algebra, Mathematisch Centrum report, ZW 14/73, Amsterdam, 1973.Google Scholar
3. Shoenneld, J. R., Mathematical logic (Addison, Wesley, Reading, Massachusetts, 1967).Google Scholar
4. Sikorski, R., Boolean algebras, third edition (Berlin, 1969).Google Scholar