FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 1, PAGES 35-44

An example of two cardinals that are equivalent in the $n$-order logic and not equivalent in the $(n+1)$-order logic

V. A. Bragin and E. I. Bunina

Abstract

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It is proved that the property of two models to be equivalent in the $n$th order logic is definable in the $(n+1)$th order logic. Basing on this fact, there is given an (nonconstructive) "example" of two $n$-order equivalent cardinal numbers that are not $(n+1)$-order equivalent.

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Last modified: September 5, 2013