Representation and preservation of the metamathematical quotients of A. Robinson
The concept of metamathematical ideal in structures, developed by A. Robinson, generalizes the notion of (algebraic) congruence in two ways: it takes into account the predicates of the language, and also it is defined relatively to a given theory. A concept of quotient follows. This paper solves the problem of characterizing the theories preserving these quotients, raised by \textit{A. F. Margarit} and \textit{L. M. Laita} [Z. Math. Logik Grundlagen Math. 33, 497-505 (1987; Zbl 0639.03036)]. It is found that such theories are those equivalent to a union of Positive and of Universal Strict Horn sentences (by showing first that the class \(Q(T^*)\) of the quotients of all models of \(T\) is \(H(T^*)\cap\text{SP}(T^*)\)).
scientific article; zbMATH DE number 203159