Une procédure de décision pour un problème de satisfiabilité dans un univers ensembliste héréditairement fini
We prove that the set of asymptotic critical values of a function definable in an o-minimal structure is finite, even if the structure is not polynomially bounded. As a consequence, the function is a locally trivial fibration over the complement of this set.
A characterization of locally finite congruence modular varieties with the number of at most k-generated models being bounded from above by a polynomial in k is given. These are exactly the varieties polynomially equivalent to the varieties of unitary modules over a finite ring of finite representation type.
We introduce the notion of a weak generic type in a group. We improve our earlier results on countable coverings of groups and types.
We prove that there exists a structure M whose monadic second order theory is decidable, and such that the first-order theory of every expansion of M by a constant is undecidable.
We give some examples of polynomially bounded o-minimal expansions of the ordered field of real numbers where the Weierstrass division theorem does not hold in the ring of germs, at the origin of ℝⁿ, of definable functions.