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Continuous Theories

  • Stephen L. Bloom
  • Zoltán Ésik
Part of the EATCS Monographs on Theoretical Computer Science book series (EATCS)

Abstract

In the first three sections of this chapter we consider theories whose hom-sets are equipped with a partial order which is compatible with the theory operations; iteration is defined using least fixed points. An ordered theory is a special kind of 2-theory, one in which there is a vertical morphism fg iff f ω g. In Section 4, the connection between initiality and the fixed point properties of iteration is examined in the context of 2-theories. We consider the properties of initial f-algebras, for horizontal morphisms f in a 2-theory. Many properties of iteration theories hold when all such initial algebras exist. In the last section, some of the constructions for ω-continuous ordered theories are generalized to ω-continuous 2-theories. In particular, it is shown how any ω-continuous 2-theory determines an iteration theory.

Keywords

Continuous Theory Rational Theory Parameter Identity Iteration Equation Pairing Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Stephen L. Bloom
    • 1
  • Zoltán Ésik
    • 2
  1. 1.Department of Computer ScienceStevens Institute of TechnologyHobokenUSA
  2. 2.Department of Computer ScienceA. József UniversitySzegedHungary

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