Gödel incompleteness in AF C*-algebras

DOI10.1515/FORUM.2008.048zbMath1163.46036MaRDI QIDQ3546146

Daniele Mundici, Constantine Tsinakis

Publication date: 18 December 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

zbMATH Keywords

undecidableAF \(C^*\)-algebraeffectively enumerableElliott partial monoid

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Computability and recursion theory (03D99) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (6)

Word problems in Elliott monoids ⋮ Revisiting the Farey AF algebra ⋮ Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups ⋮ Finite axiomatizability in Łukasiewicz logic ⋮ Interpretation of De Finetti coherence criterion in Łukasiewicz logic ⋮ Recognizing the Farey-Stern-Brocot AF algebra

Cites Work

• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• On the classification of inductive limits of sequences of semisimple finite-dimensional algebras
• Prime ideals in free \(\ell\)-groups and free vector lattices
• Reconstructing \(C^*\)-algebras from their Murray von Neumann orders
• \(C^ *\)-algebras with a two-point dual
• Simple Bratteli diagrams with a Gödel-incomplete C*-equivalence problem
• Non-stationarity of isomorphism between AF algebras defined by stationary Bratteli diagrams
• Free Sums of Groups and Their Generalizations. An Analysis of the Associative Law

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