Amorphous models

Resumo

An interpretation (model) for a first order language is amorphous provided every transformation on its domain is an automorphism. Among amorphous interpretations are all models of the theory of the universal binary relation. Here it is shown that many of the well known model theoristic properties of such examples hold for all amorphous interpretations: (I) that each non-logical constant is definable in the complete theory of an amorphous interpretantion by a boolean combination of quantifier free formulas in a pure identify language; (2) that the complete of an theory of amorphous interpretation admits elimination of quantifiers; (3) that the complete theory of na infinite amorphous interpretation is totally categorical, not finitely axiomatizable, the model completion of ∏0 1 theory, and axiomatizable by its ∏0 1theory and na infinite set of ∑0 1sentences stating that for each in its domain is of cardinality at least n; and (4) that all infinite amorphous interpretations of a first order language with finite non-logical vocabular are quase-finitely axiomatizable.