On the Definitional Embeddability of Some Elementary Algebraic Theories into the First-Order Predicate Calculus
##plugins.themes.bootstrap3.article.main##
Abstract
In this article we prove a theorem on the definitional embeddability into first-order predicate logic without equality of such well-known mathematical theories as group theory and the theory of Abelian groups. This result may seem surprising, since it is generally believed that these theories have a non-logical content. It turns out that the central theory of general algebra are purely logical. Could this be the reason that we find them in many branches of mathematics? This result will be of interest not only for logicians and mathematicians but also for philosophers who study foundations of logic and its relation to mathematics.
##plugins.generic.usageStats.downloads##
##plugins.generic.usageStats.noStats##
##plugins.themes.bootstrap3.article.details##
How to Cite
Shalack V. I. On the Definitional Embeddability of Some Elementary Algebraic Theories into the First-Order Predicate Calculus // Logicheskie Issledovaniya / Logical Investigations. 2015. VOL. 21. № 2. C. 15-20.
Issue
Section
Papers
References
Karpovich, V.N. Terminy v strukture teorii. Logicheskij analiz [Terms in the structure of the theory. Logical analysis]. Novosibirsk: Nauka, 1978. 128 pp. (In Russian)
Mendelson, E. Vvedenie v matematicheskuyu logiku [Introduction to Mathematical Logic], 4-th ed., M.: Nauka, 1997. 440 pp. (In Russian)
Smirnov, V.A. “Logical Relations between Theories”, Synthese, 1986, 66(1), pp. 71–87.
Shalack, V. “On Some Applied First-Order Theories which Can be Represented by Definitions”, Bulletin of the Section of Logic, 2015, 44/1-2, pp. 19–24.
Mendelson, E. Vvedenie v matematicheskuyu logiku [Introduction to Mathematical Logic], 4-th ed., M.: Nauka, 1997. 440 pp. (In Russian)
Smirnov, V.A. “Logical Relations between Theories”, Synthese, 1986, 66(1), pp. 71–87.
Shalack, V. “On Some Applied First-Order Theories which Can be Represented by Definitions”, Bulletin of the Section of Logic, 2015, 44/1-2, pp. 19–24.