Horn theories with nonmaximal spectrum

The axiomatic closure of the class of discriminating groups

“…Hence by Los-Suszko [10] it has at least one set of universal-existential axioms. Also, the class of squarelike groups is closed under reduced products (also see [6]); so, by an observation of E. Palyutin and S. Starchenko [14], it is a Horn class. A and B are groups, then we say that A and B are n-elementarily equivalent denoted A ≡ n B if A and B satisfy the same prenex normal form sentences of L 0 involving no more than n − 1 alternations of quantifier type.…”

Discrimination in a General Algebraic Setting

“…It follows that the class of squarelike algebras in 𝒱 is preserved under taking reduced products. Now, as mentioned in page 225 of [ 11 ], an axiomatic class closed under reduced products has a set of Horn axioms. That completes the proof.…”

Categorical horn classes. 2

“…2), we conclude that there exists a map f 0 : θ 1 a 0 → θ 1 b 0 , preserving truth of primitive formulas and their negations. Consider models M eh and N eh (see [5]). Let f : X → N eh be a maximal (w.r.t.…”

“…We know from [5,7] that if a primitive normal structure A has additively connected primitive sets then a nontrivial group is primitive interpreted in the structure A. THEOREM 6. Let K be a categorical Horn class in which no nontrivial group is primitive interpreted.…”