Transforming structures by set interpretations

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Thomas Colcombet, Christof Löding
• Keywords: CORR 2007, Education, Interpretations, finite Sets, finite Sets Interpretations