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Coordinatization of Countable MV algebras

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If you have a question about this talk, please contact Tamara von Glehn.

The algebras of many-valued Lukasiewicz logics (MV algebras) as well as the algebras of quantum measurement (Effect algebras) have undergone major development since the 1980s and 1990s. They have recently attracted the attention of categorists.

I will give a brief introduction to MV algebras, as well as the more general world of effect algebras. Time permitting, I hope to illustrate these notions by sketching recent results (with Mark Lawson, Heriot-Watt) on coordinatization of countable MV-algebras using inverse semigroup theory. The structures involved, Boolean inverse monoids, have recently arisen in areas related to non-commutative Stone duality, aperiodic tilings, etc. We prove that every countable MV algebra is isomorphic to the lattice of principal ideals of certain Boolean inverse monoids. The specific class involved in the proof, AF inverse monoids, corresponds to AF C *-algebras and arises from Bratteli diagrams of countable dimension groups. If there’s time, further new directions by F. Wehrung, D. Mundici, et. al. will be discussed.

This talk is part of the Category Theory Seminar series.

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