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Hierarchies based on objects of finite type1

Published online by Cambridge University Press:  12 March 2014

Thomas J. Grilliot
Thomas J. Grilliot*
Affiliation:
Duke University Pennsylvania State University
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Extract

Shoenfield [8] has shown that a hierarchy for the functions recursive in a type-2 object can be set up whenever E2 (the type-2 object that introduces numerical quantification) is recursive in that type-2 object. With a restriction that we will discuss in the next paragraph, Moschovakis [4, pp. 254–259] has solved the analogous problem for type-3 objects. His method seems to generalize for any type-n object, where n ≥ 2. We will solve this same problem of finding hierarchies based on type-n objects by a different method. Instead of using ordinal notations for indexing stages of hierarchies, as do Shoenfield and Moschovakis, we will define notation-independent stages.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 2 , 25 July 1969 , pp. 177 - 182
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

The results in this paper are substantially contained in the author's doctoral dissertation written under the supervision of J. R. Shoenfield and supported by an N.S.F. grant.

References

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