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Provability in predicate product logic

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Abstract

We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic, \({\Pi\forall}\) . By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from \({\Pi\forall}\) if and only if it is an L-tautology. As well we characterize the class of lexicographic sums that have this universality property.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Michael C. Laskowski

  2. Department of Mathematics, University of Wisconsin, Madison, Madison, WI, 53706, USA

    Shirin Malekpour

Authors
  1. Michael C. Laskowski
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  2. Shirin Malekpour
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Corresponding author

Correspondence to Michael C. Laskowski.

Additional information

Partially supported by NSF grant DMS-0300080.

Portions of this material appears in Malekpour’s doctoral dissertation.

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Laskowski, M.C., Malekpour, S. Provability in predicate product logic. Arch. Math. Logic 46, 365–378 (2007). https://doi.org/10.1007/s00153-007-0036-4

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  • DOI: https://doi.org/10.1007/s00153-007-0036-4

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