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On analytic well-orderings

Published online by Cambridge University Press:  12 March 2014

Hisao Tanaka
Hisao Tanaka*
Affiliation:
Hosei University, Koganei, Tokyo, Japan
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Extract

Since about 1955, recursive, (hyper-)arithmetic and well-orderings have been investigated by many authors. Now we shall generally consider analytic well-orderings and compare their representation-capacities for ordinals.

Let K be a class of predicates. Then, R is called a Kwell-ordering if R is a binary relation of natural numbers belonging to the class K and satisfies the following conditions:

(i) R(x, y) ∧ R(y, x) → x = y;

(ii) x, y ∈ D(R) → R(x, y) ∨ R(y, x), where D(R) is the domain of R, that is to say, the set {x ∣ (∃y)[R(x, y) ∨ R(y, x)]};

(iii) R(x, y) ∧ R(y, z) → R(x, z);

(iv) .

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 2 , June 1970 , pp. 198 - 204
Copyright
Copyright © Association for Symbolic Logic 1970

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