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- Peter Aczel, Nax Paul Mendler
- Category Theory and Computer Science
- 1989

We prove that every set-based functor on the category of classes has a final coalgebra. This result strengthens the final coalgebra theorem announced in the book "Non-well-founded Sets", by the first author. 1 I n t r o d u c t i o n The theorem of this note is an improvement of a result that was first stated, but not proved in its full generality, in… (More)

- Peter Aczel, P. ACZEL
- 2008

INTRODUCTION Intuitionistic mathematics can be structured into two levels. The first level arises directly out of Brouwer's criticism of certain methods and notions of classical mathematics. the law of excluded middle was rejected and instead the meaning of mathematical statements was to be based on the notion of 'proof'. level of intuitionism was a theory… (More)

- J C M Baeten, T Basten, +7 authors Frontmatter More
- 2010

Process algebra is a widely accepted and much used technique in the specification and verification of parallel and distributed software systems. This book sets the standard for the field. It assembles the relevant results of most process algebras currently in use, and presents them in a unified framework and notation. The authors describe the theory… (More)

- P. Aczel, M. Rathjen
- 2008

4 Operations on Sets and Classes 25 4.1 Class Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Class Relations and Functions . . . . . . . . . . . . . . . . . . 26 4.3 Some Consequences of Union-Replacement . . . . . . . . . . . 27 4.4 Russell’s paradox . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 Subset Collection and… (More)

- Peter Aczel, Jirí Adámek, Stefan Milius, Jiri Velebil
- Theor. Comput. Sci.
- 2003

In#nite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has #nal coalgebras for all functors H ( ) + X , then those coalgebras, TX… (More)

- Peter Aczel
- J. Symb. Log.
- 1972

- Peter Aczel
- Ann. Pure Appl. Logic
- 2006

- Peter Aczel
- MFPS
- 1993

We describe the nal universe approach to the character-isation of semantic universes and illustrate it by giving char-acterisations of the universes of CCS and CSP processes.

- Peter Aczel
- TYPES
- 1998

Introduction The original motivation 1 for the work described in this paper was to determine the proof theoretic strength of the type theories implemented in the proof development systems Lego and Coq, Luo and Pollack 92, Barras et al 96]. These type theories combine the impredicative type of propositions 2 , from the calculus of constructions, Coquand 90],… (More)

- Peter Aczel
- Mathematical Structures in Computer Science
- 2001