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Positive Sugihara monoids

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Abstract.

It is proved that in the variety of positive Sugihara monoids, every finite subdirectly irreducible algebra is a retract of a free algebra. It follows that every quasivariety of positive Sugihara monoids is a variety, in contrast with the situation in several neighboring varieties. This result shows that when the logic R-mingle is formulated with the Ackermann constant t, then its full negation-free fragment is hereditarily structurally complete.

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Authors and Affiliations

  1. Department of Mathematics, Norwich University, 158 Harmon Dr., Northfield, VT, 05663, USA

    Jeffrey S. Olson

  2. School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa

    James G. Raftery

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  1. Jeffrey S. Olson
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  2. James G. Raftery
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Correspondence to Jeffrey S. Olson.

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Received August 28, 2005; accepted in final form July 31, 2006.

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Olson, J.S., Raftery, J.G. Positive Sugihara monoids. Algebra univers. 57, 75–99 (2007). https://doi.org/10.1007/s00012-007-2022-4

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  • DOI: https://doi.org/10.1007/s00012-007-2022-4

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