Abstract
We consider pseudofinite MV-algebras. As a main result, we show that an infinite MV-algebra is pseudofinite if and only if it is definably well founded, improving a result of a previous paper. Moreover, we show that the theory of pseudofinite MV-algebras has a partial form of elimination of quantifiers. Further, we show that the class of pseudofinite MV-chains and the class of pseudofinite MV-algebras are not finitely axiomatizable, we give some collapsing results for pseudofinite MV-algebras, we consider relative subalgebras of pseudofinite MV-algebras, and we study ideals of pseudofinite MV-algebras.
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Notes
We stick to the tradition of calling a structure pseudofinite only when it is infinite.
b/n does not exist in A in general, but by Theorem 3.1, A can be embedded in an MV-algebra where it exists.
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The authors are extremely grateful to the referees for their valuable comments and helpful suggestions which help to improve the presentation of this paper.
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Farsimadan, E., Lenzi, G., Rizzo, P. et al. A characterization of pseudofinite MV-algebras. Soft Comput 24, 8751–8761 (2020). https://doi.org/10.1007/s00500-020-04910-y
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DOI: https://doi.org/10.1007/s00500-020-04910-y