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In [Mon11] are studied, for the axiomatic extensions of the monoidal t-normbased logic ([EG01]), the properties of single chain completeness. On the otherside, in [GJKO07, Chapter 5] are studied many logical and algebraic properties(like Halld\'en completeness, variable separation properties, amalgamationproperty etc.), in the context of substructural logics. The aim of this paperis twofold: first of all we will specialize the properties studied in [GJKO07,Chapter 5] from the case of substructural logics to the one of extensions ofMTL, by obtaining some general characterization. Moreover we will show thatsome of these properties are indeed strictly connected to the topics developedin [Mon11]. This will help to have a better intuition concerning some openproblems of [Mon11].

On some logical and algebraic properties of axiomatic extensions of the monoidal t-norm based logic MTL related with single chain completeness