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Rich co-ordinals, addition isomorphisms, and RETs1

Published online by Cambridge University Press:  12 March 2014

Alfred B. Manaster
Alfred B. Manaster*
Affiliation:
Massachusetts Institute of Technology and Institute for Defense Analyses
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Extract

In this paper a special type of co-ordinal, called rich, is studied. Basic properties of rich co-ordinals are proved in §1. In §2 rich co-ordinals are seen to be the co-ordinals occurring in paths which are addition isomorphic to initial segments of the classical ordinals. The results of §1 are applied to obtain information about and examples of such paths. In the next section the order types of rich co-ordinals with a given field, X, is seen to be determined essentially by the finite divisors of X. RETs satisfying various divisibility conditions are constructed in §4.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 1 , 29 May 1969 , pp. 45 - 52
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

Part of the research reported here was supported under NSF grant GP 6982.

References

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