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ABSTRACT INDUCTIVE AND CO-INDUCTIVE DEFINITIONS

Published online by Cambridge University Press:  01 August 2018

GIOVANNI CURI*
Affiliation:
VIA BOITO, 23 - 35122 PADOVA, ITALYE-mail:giovanni.curi@email.it

Abstract

In [G. Curi, On Tarski’s fixed point theorem. Proc. Amer. Math. Soc., 143 (2015), pp. 4439–4455], a notion of abstract inductive definition is formulated to extend Aczel’s theory of inductive definitions to the setting of complete lattices. In this article, after discussing a further extension of the theory to structures of much larger size than complete lattices, as the class of all sets or the class of ordinals, a similar generalization is carried out for the theory of co-inductive definitions on a set. As a corollary, a constructive version of the general form of Tarski’s fixed point theorem is derived.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2018 

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Footnotes

Dedicated to Peter Aczel, on the occasion of his 75th birthday.

References

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