Abstract.
We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms.
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Received: 7 January 2002 / Revised version: 4 April 2002 / Published online: 19 December 2002
RID="*"
ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782).
Mathematics Subject Classification (2000): 20M14, 06F05
Key words or phrases: Residuated lattice – Conjunction for non-classical logics
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Jenei, S. On the structure of rotation-invariant semigroups. Arch. Math. Logic 42, 489–514 (2003). https://doi.org/10.1007/s00153-002-0165-8
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DOI: https://doi.org/10.1007/s00153-002-0165-8