We show in this paper that the theory of ordinal addition of any fixed ordinal ωα, with α less than ωω, admits a quantifier elimination. This in particular gives a new proof for the decidability result first established in 1965 by R. Büchi using transfinite automata. Our proof is based on the Ehrenfeucht games, and we show that quantifier elimination go through generalized power.RésuméOn montre ici que, pour tout ordinal α inférieur à ωω, la théorie additive de ωα admet une (...) élimination des quantificateurs. On obtient ainsi une nouvelle preuve de la décidabilité de ces théories . On utilise ici les jeux d'Ehrenfeucht, avec un formalisme à la Ferrante et Rackoff, et on montre que le fait d'admettre une élimination des quantificateurs se transmet par produit généralisé. (shrink)

We develop a category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in the topology of compact Hausdorff spaces.

We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.

We characterise the class S Ra CA n of subalgebras of relation algebra reducts of n -dimensional cylindric algebras by the notion of a ‘hyperbasis’, analogous to the cylindric basis of Maddux, and by representations. We outline a game–theoretic approximation to the existence of a representation, and how to use it to obtain a recursive axiomatisation of S Ra CA n.

Assuming certain conditions on a class equation image of finitely generated first-order structures admitting the model-theoretical construction of a Fraïssé limit, we characterize retracts of such limits as algebraically closed structures in a class naturally related to equation image. In this way we generalize an earlier description of retracts of the countably infinite random graph.