Abstract
We explore connections between elementary equivalence of categories of acts over monoids and second-order equivalence of monoids.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. I. Mal’tsev, “Elementary properties of linear groups,” in Some Problems in Mathematics and Mechanics [in Russian], SO AN SSSR, Novosibirsk (1961), pp. 110–132.
C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam (1973).
C. I. Beidar and A. V. Mikhalev, “On Malcev’s theorem on elementary equivalence of linear groups,” Cont. Math., 131, 29–35 (1992).
E. I. Bunina, “Elementary equivalence of unitary linear groups over rings and skew,” Usp. Mat. Nauk, 53, No. 2, 137–138 (1998).
E. I. Bunina, “Elementary equivalence of Chevalley groups,” Usp. Mat. Nauk, 56, No. 1, 157–158 (2001).
E. I. Bunina, “Chevalley groups over fields and their elementary properties,” Usp. Mat. Nauk, 59, No. 5, 952–953 (2004).
V. Tolstykh, “Elementary equivalence of infinite-dimensional classical groups,” Ann. Pure Appl. Log., 105, 103–156 (2000).
E. I. Bunina and A. V. Mikhalev, “Elementary equivalence of categories of modules over rings, endomorphism rings, and automorphism groups of modules,” Fund. Prikl. Mat., 10, No. 2, 51–134 (2004).
E. I. Bunina and A. V. Mikhalev, “Elementary equivalence of endomorphism rings of Abelian p-groups,” Fund. Prikl. Mat., 10, No. 2, 135–224 (2004).
M. Kilp, U. Knauer, and A. V. Mikhalev, Monoids, Acts and Categories, Walter de Gruyter, Berlin (2000).
Author information
Authors and Affiliations
Additional information
__________
Translated from Algebrai Logika, Vol. 45, No. 6, pp. 687–709, November–December, 2006.
Rights and permissions
About this article
Cite this article
Bunina, E.I., Mikhalev, A.V. Elementary properties of categories of acts over monoids. Algebr Logic 45, 389–402 (2006). https://doi.org/10.1007/s10469-006-0036-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10469-006-0036-1