The Quasi-lattice of Indiscernible Elements

Authors:
Mauri Cunha Do Nascimento;Décio Krause;Hércules Araújo Feitosa
Affiliations:
São Paulo State University, São Paulo, Brasil;Santa Catarina Federal University, Florianópolis, Brasil;São Paulo State University, São Paulo, Brasil
Venue:
Studia Logica
Year:
2011

Citing 4
Cited 0

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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.