Amador Martin-Pizarro

Learn More
We exhibit a simplified version of the construction of a field of Morley rank p with a predicate of rank p − 1, extracting the main ideas for the construction from previous papers and refining the arguments. Moreover, an explicit axiomatization is given, and ranks are computed.
Wir betrachten zwei abzählbare streng–minimale Theorien T1 und T2 mit definierbarem Morleygrad, formuliert in zwei disjunkten Sprachen L1 und L2. Wir beweisen in diesem Artikel den folgenden Satz von E. Hrushovski. Satz 0.1 ([2]). T1 ∪ T2 hat eine streng minimale Vervollständigung T. Die Modelle M von T haben die folgenden Eigenschaft: tri bezeichne den(More)
The above theorem was proved by extending Fräıssé’s amalgamation procedure to a given class in which Hrushovski’s “δ–function” will determine the pregeometry. In order to axiomatize the theory of the generic model, a set of representatives of rank 1 types or “codes” is chosen in a uniform way. From now on, let F denote a fixed finite field and T0 the theory(More)
In this text elements of motivic integration are discussed, mostly with full proofs. The main sources are original papers by Denef-Loeser [2, 3]. There exist several survey articles on motivic integration: [10], [12], [11], [9], [13], [14]. Throughout the text k is any field. Let X,Y be varieties over k; let A,B be constructible subsets of X,Y respectively.(More)
En 1991, Hrushovski [7, 5] donna une preuve de la conjecture de Mordell-Lang pour les corps de fonctions. Ce résultat était déjà connu en caractéristique nulle, mais l’originalité de cette nouvelle preuve réside dans son approche uniforme en toutes caractéristiques. Elle consiste à remplacer la structure du corps algébriquement clos de base, par une(More)
  • 1