Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperstates of Involutive MTL-Algebras that Satisfy $(2x)^2 = 2(x^2)$   States of MV-algebras have been the object of intensive study and attempts of
generalizations. The aim of this contribution is to provide a preliminary
investigation for states of prelinear semihoops and hyperstates of algebras in
the variety generated by perfect and involutive MTL-algebras (IBP0-algebras for
short). Grounding on a recent result showing that IBP0-algebras can be
constructed from a Boolean algebra, a prelinear semihoop and a suitably defined
operator between them, our first investigation on states of prelinear semihoops
will support and justify the notion of hyperstate for IBP0- algebras and will
actually show that each such map can be represented by a probability measure on
its Boolean skeleton, and a state on a suitably defined abelian l-group.

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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an