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On universal algebra over nominal sets

  • ALEXANDER KURZ (a1) and DANIELA PETRIŞAN (a1)
Abstract

We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full reflective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a ‘uniform’ fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into ‘uniform’ theories, and systematically prove HSP theorems for models of these theories.

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References
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F. Borceux (1994) Handbook of Categorical Algebra, Cambridge University Press.

M. P. Fiore and C.-K. Hur (2008) Term equational systems and logics (extended abstract). Electronic Notes in Theoretical Computer Science 218 171192.

M. Gabbay (2008) Nominal algebra and the HSP theorem. Journal of Logic and Computation 19 (2) 341367.

A. Kurz and D. Petrişan (2008) Functorial coalgebraic logic: The case of many-sorted varieties. In: J. Adámek and C. Kupke (eds.) Proceedings of the Ninth Workshop on Coalgebraic Methods in Computer Science (CMCS 2008). Electronic Notes in Theoretical Computer Science 203 (5) 175194

I. Stark (2008) Free-algebra models for the pi -calculus. Theoretical Computer Science 390 (2-3) 248270.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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