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Isomorphisms and nonisomorphisms of graph models

Published online by Cambridge University Press:  12 March 2014

Harold Schellinx*
Department of Mathematics and Computer Science, University of Amsterdam, Amsterdam, The Netherlands


In this paper the existence or nonexistence of isomorphic mappings between graph models for the untyped lambda calculus is studied. It is shown that Engeler's is DA completely determined, up to isomorphism, by the cardinality of its ‘atom-set’ A. A similar characterization is given for a collection of graph models of the -type; from this some propositions regarding automorphisms are obtained. Also we give an indication of the complexity of the first-order theory of graph models by showing that the second-order theory of first-order definable elements of a graph model is first-order expressable in the model.

Research Article
Copyright © Association for Symbolic Logic 1991

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