) St'ephane Grumbach I.N.R.I.A. Rocquencourt BP 105 78153 Le Chesnay, France email@example.com Jianwen Su Computer Science Department University of California Santa Barbara, California 93106, USA firstname.lastname@example.org Abstract We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. The mathematical framework is based on classical decidable first-order theories. We investigate the theory of finitely representable models and prove that it differs strongly from both classical model theory and finite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the definability of queries in the relational calculus over finitely representable databases. We illustrate this very challenging problem through some classical examples. 1 I..