On free MV algebras and a problem of Tarski (Q2813678)

MV algebras stand to Łukasiewicz infinite-valued logic as Boolean algebras stand to classical logic. They form an equational class and, by the present reviewer's result in his paper [J. Funct. Anal. 65, 15--63 (1986; Zbl 0597.46059)], MV algebras are categorically equivalent to lattice-ordered abelian groups with a distinguished order unit. Let \(T_k\) be the first-order theory of free MV-algebras over \(k\) free generators. In the paper under review, the authors prove that \(T_k\neq T_h\) for \(k\neq h\). This is a reminiscent of Tarski's problem for free groups of different rank. \textit{Z. Sela} solved this problem in his paper [Geom. Funct. Anal. 16, No. 3, 707--730 (2006; Zbl 1118.20035)].NEWLINENEWLINEFor background on MV-algebras see [\textit{R. L. O. Cignoli} et al., Algebraic foundations of many-valued reasoning. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0937.06009)]. For advanced topics see the present reviewer's monograph [Advanced Łukasiewicz calculus and MV-algebras. Berlin: Springer (2011; Zbl 1235.03002)].