In this paper closure theory is applied in order to obtain a uniform semantical treatment of both primitive and general iteration. In particular, the theory of Peano algebras has been extended to algebraic structures to inductively define both primitive and general iterates as structure homomorphisms, i.e. as fixed points of iteration equations
International audienceIn the early seventies, Shelah proposed a model-theoretic construction, nowada...
AbstractThis paper extends Part 1 of the paper with the same title. Here, matricial iteration theori...
AbstractThe concept of iteration theory of Bloom and Ésik summarizes all equational properties that ...
AbstractThe equational class generated by rational algebraic theories was characterized in Esik, Com...
“In the setting of algebraic theories enriched with an external fixed-point operation, the no-tion o...
We prove the following completeness theorem: If the fixed point operation over a category is defined...
AbstractWe prove the following completeness theorem: If the fixed point operation over a category is...
All known structures involving a constructively obtainable fixed point (or it-eration) operation sat...
We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operato...
Abstract. A Peano σ-algebra generated by a set M, denoted by M, is a set of words over the alphabet ...
AbstractThe (in)equational properties of iteration, i.e., least (pre-)fixed point solutions over cpo...
Abstract. Iteration exists extensively in the nature. Iteration of a homeo-morphism generates a dyna...
This paper deals with solutions of algebraic, linear, and rational systems of equations over an -com...
The axioms of iteration 2-theories capture, up to isomorphism, the equational properties of iteratio...
Abstract. A computer implementation of Gödel’s algorithm for class formation in Mathematica TM was u...
International audienceIn the early seventies, Shelah proposed a model-theoretic construction, nowada...
AbstractThis paper extends Part 1 of the paper with the same title. Here, matricial iteration theori...
AbstractThe concept of iteration theory of Bloom and Ésik summarizes all equational properties that ...
AbstractThe equational class generated by rational algebraic theories was characterized in Esik, Com...
“In the setting of algebraic theories enriched with an external fixed-point operation, the no-tion o...
We prove the following completeness theorem: If the fixed point operation over a category is defined...
AbstractWe prove the following completeness theorem: If the fixed point operation over a category is...
All known structures involving a constructively obtainable fixed point (or it-eration) operation sat...
We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operato...
Abstract. A Peano σ-algebra generated by a set M, denoted by M, is a set of words over the alphabet ...
AbstractThe (in)equational properties of iteration, i.e., least (pre-)fixed point solutions over cpo...
Abstract. Iteration exists extensively in the nature. Iteration of a homeo-morphism generates a dyna...
This paper deals with solutions of algebraic, linear, and rational systems of equations over an -com...
The axioms of iteration 2-theories capture, up to isomorphism, the equational properties of iteratio...
Abstract. A computer implementation of Gödel’s algorithm for class formation in Mathematica TM was u...
International audienceIn the early seventies, Shelah proposed a model-theoretic construction, nowada...
AbstractThis paper extends Part 1 of the paper with the same title. Here, matricial iteration theori...
AbstractThe concept of iteration theory of Bloom and Ésik summarizes all equational properties that ...
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