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Paper   IPM / M / 16000
School of Mathematics
  Title:   Axiomatizing mathematical theories: Multiplication
  Author(s):  Saeed Salehi
  Status:   In Proceedings
  Proceeding: Proceedings of Frontiers in Mathematical Sciences
  Year:  2012
  Pages:   165-176
  Supported by:  IPM
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some mathematical structures are now classical theorems in Logic, Algebra and Geometry. In this paper we will study the axiomatizability of the theories of multiplication in the domains of natural, integer, rational, real, and complex numbers. We will review some classical theorems, and will give some new proofs for old results. We will see that some structures are missing in the literature, thus leaving it open whether the theories of that structures are axiomatizable (decidable) or not. We will answer one of those open questions in this paper.

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