Dagger extension theorem

Z. Ésik, T. Hajgató

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Partial iterative theories are algebraic theories such that for certain morphisms f the equation Ξ = f · 〈Ξ, 1p〉 has a unique solution. Iteration theories are algebraic theories satisfying a certain set of identities. We investigate some similarities between partial iterative theories and iteration theories. In our main result, we give a sufficient condition ensuring that the partially defined dagger operation of a partial iterative theory can be extended to a totally defined operation so that the resulting theory becomes an iteration theory. We show that this general extension theorem can be instantiated to prove that every Elgot iterative theory with at least one constant morphism 1 → 0 can be extended to an iteration theory. We also apply our main result to theories equipped with an additive structure.

Original languageEnglish
Pages (from-to)1035-1066
Number of pages32
JournalMathematical Structures in Computer Science
Volume21
Issue number5
DOIs
Publication statusPublished - Oct 1 2011

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Computer Science Applications

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