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The Quasi-lattice of Indiscernible Elements

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Abstract

The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice (\({\mathfrak{I}}\)-lattice), which can be modeled by an algebraic structure built in quasi-set theory \({\mathfrak{Q}}\) . This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that ‘naturally’ arises is non distributive.

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Authors and Affiliations

  1. São Paulo State University, São Paulo, Brasil

    Mauri Cunha do Nascimento & Hércules de Araújo Feitosa

  2. Santa Catarina Federal University, Florianópolis, Brasil

    Décio Krause

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  1. Mauri Cunha do Nascimento
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  2. Décio Krause
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  3. Hércules de Araújo Feitosa
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Correspondence to Mauri Cunha do Nascimento.

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Cunha do Nascimento, M., Krause, D. & de Araújo Feitosa, H. The Quasi-lattice of Indiscernible Elements. Stud Logica 97, 101–126 (2011). https://doi.org/10.1007/s11225-010-9300-4

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