Questioni di teoria dei modelli per linguaggi universali positivi. II: Metodi di "back and forth"

Tulipani, Sauro

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 59 (1975) no. 5, pp. 328-335

Résumé

In this paper we continue the investigations of a previous one, givinga back and forth characterization of L—equivalence, where L is an universal positive (u.p.)language. The key idea is to use partial abridgments in place of partial isomorphisms. This allows us to proceed in the same way as in the classical characterization of elementary equivalence. These results and those (1) by Barwise and Schlipf on recursively saturated models are used to get a Robinson Consistency Theorem for u.p. and negation of u.p. sentences. It follows that, given u.p. or negation of u.p. sentences $\alpha,\beta$, the interpolating sentence can be chosen u.p. or negation of u.p. Finally we discuss Craig's Theorem for u.p. languages.