The Turing complexity of AF C*-algebras with lattice-ordered KO

  • Daniele Mundici
Part of the Lecture Notes in Computer Science book series (LNCS, volume 270)


Approximately finite-dimensional (AF) C⋆-algebras were introduced in 1972 by Bratteli, generalizing earlier work of Glimm and Dixmier. In a recent paper, the author presents a natural one-one correspondence between Lindenbaum algebras of the infinite-valued sentential calculus of Łukasiewicz, and AF C⋆-algebras whose Grothendieck group (KO) is lattice-ordered. Thus, any such algebra \(\mathfrak{A}\) can be encoded by some theory Φ in the Łukasiewicz calculus, and Φ uniquely determines \(\mathfrak{A}\), up to isomorphism. In the present paper, Glimm's universal UHF algebra, the Canonical Anticommutation Relation (CAR) algebra, and the Effros-Shen algebras corresponding to quadratic irrationals are explicitly coded by theories whose decision problems are solvable in deterministic polynomial time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Daniele Mundici
    • 1
  1. 1.Loc.Romola N.76 50060 DonniniFlorenceItaly

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