Abstract:

Degrees of semantic and syntactic rigidity are important characteristics of any structure. Semantic rigidity indicates how close a given structure is to a structure with a singleton automorphism group; syntactic rigidity indicates how close a given structure is to a structure that is the definable closure of the empty set. In this paper we study the semantic and syntactic rigidities of unars, including those satisfying the properties of injectivity and projectivity and their weakened forms: weakly-, quasi-, and pseudo-injectivity, weakly-, quasi-, and pseudo-projectivity. All possible values of pairs of semantic and syntactic rigidity for such unars are described.