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Math. Logic"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes\u2019 property. We show that an MV-algebra admits a state with the Bayes\u2019 property if and only if it is bipartite.<\/jats:p>","DOI":"10.1007\/s00153-024-00926-5","type":"journal-article","created":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T19:01:30Z","timestamp":1715194890000},"page":"893-919","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Spectral MV-algebras and equispectrality"],"prefix":"10.1007","volume":"63","author":[{"given":"Giuseppina Gerarda","family":"Barbieri","sequence":"first","affiliation":[]},{"given":"Antonio","family":"Di Nola","sequence":"additional","affiliation":[]},{"given":"Giacomo","family":"Lenzi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,8]]},"reference":[{"issue":"1","key":"926_CR1","first-page":"111","volume":"38","author":"R Ambrosio","year":"1993","unstructured":"Ambrosio, R., Lettieri, A.: A classification of bipartite MV-algebras. 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