Contributions to the investigations of Lascar strong types in simple theories

AUTOR(ES)
DATA DE PUBLICAÇÃO

2003

RESUMO

First, we shall prove some results about thick formulas and bounded equivalence relations, valid in arbitrary complete theories. The application of these results to simple theories yields some nice and useful properties with respect to Lascar strong types. Furthermore, we consider subclasses of simple theories, definable by dividing chains as in [CasWag]. As one of our main results we find a considerable improvement of a Theorem due to Kim (Proposition 3.6 in [Kim1], or Theorem 2.4.7.6 in [Wag]), which describes dividing by means of Morley sequences. This leads us to new and promising characterizations of the class of low theories. We study simple theories having a special property that we call the independent dividing chain property. Another main result is that simple, ω-categorical theories having this property are low. We define and study a new rank that allows characterizing short and low theories and give rise to further studies. Furthermore, we develop a rapprochement to the investigation of the equality of strong types and Lascar strong types using the preceding results about bounded equivalence relations. Finally, in the last section we develop and outline some promising ideas for further studies in simple theories proceeding from the main results of this thesis. These considerations could serve in future works to tackle open questions such as the Lstp=stp problem (equality of Lascar strong types and strong types) and may lead to a better understanding of the relationships between some subclasses of simple theories

ASSUNTO(S)

ciencia da computacao simple theories lascar strong tipes investigations

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