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

View as HTML
View as gif image

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.

Location: http://mech.math.msu.su/~fpm/eng/k13/k131/k13103h.htm

Last modified: September 5, 2013