Fixed-point extensions of first-order logic

Authors:
Yuri Gurevich;Saharon Shelah
Affiliations:
-;-
Venue:
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Year:
1985

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Abstract

We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.