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.
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References
A. L. Brudno, Theory of Real Variables Functions [in Russian], Nauka, Moscow (1971).
E. I. Bunina and A. V. Mikhalev, “Elementary equivalence of endomorphism rings of Abelian p-groups,” J. Math. Sci., 137, No. 6, 5275–5335 (2006).
C. C. Chang and H. G. Keisler, Model Theory, Am. Elsevier, New York (1973).
A. Pinus, “The Lowenheim–Skolem property for second-order logic,” in: Recursive Functions [in Russian], Ivanov. Gos. Univ., Ivanovo (1978), pp. 55–60.
B. Poizat, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Springer (2000).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 1, pp. 35–44, 2013.
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Bragin, V.A., Bunina, E.I. An Example of two Cardinals that are Equivalent in the n-Order Logic and not Equivalent in the (n + 1)-Order Logic. J Math Sci 201, 431–437 (2014). https://doi.org/10.1007/s10958-014-2002-0
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DOI: https://doi.org/10.1007/s10958-014-2002-0