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; E. I. Bunina

doi:10.1007/s10958-014-2002-0

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, E. I. Bunina

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

Abstract

It is proved that the property of two models to be equivalent in the nth 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.

Original language	English
Pages (from-to)	431-437
Number of pages	7
Journal	Journal of Mathematical Sciences
Volume	201
Issue number	4
DOIs	https://doi.org/10.1007/s10958-014-2002-0
State	Published - Sep 2014
Externally published	Yes

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An Example of two Cardinals that are Equivalent in the n-Order Logic and not Equivalent in the (n + 1)-Order Logic

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