Teoria dei campi differenziali ordinati
Lacava, Francesco
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975), p. 322-327 / Harvested from Biblioteca Digitale Italiana di Matematica
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In this paper we study the theory of ordered differential fields (CDO); in other words, the theory obtained adding the order axioms for a field to "differential field" 's axioms. If we consider a model K of such theory and we "forget" order, we know that such model is embedded in its differential closure. In a such closure, we can consider the set of real fields. Such a set has maximal elements (with respect to inclusion). We call CDO* the theory of so obtained maximal elements, for all K∈M⁢o⁢d (CDO). If we neglect derivation, models of CDO* are real closed and then ordered. So we can prove that CDO* is the model completion of CDO. We find the axioms of CDO*, too. Finally, we find a method for eliminating quantifiers (for CDO*) in the formulas containing only inequalities.

Publié le : 1975-11-01
@article{RLINA_1975_8_59_5_322_0,
     author = {Francesco Lacava},
     title = {Teoria dei campi differenziali ordinati},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {59},
     year = {1975},
     pages = {322-327},
     zbl = {0353.02032},
     mrnumber = {0480009},
     language = {it},
     url = {http://dml.mathdoc.fr/item/RLINA_1975_8_59_5_322_0}
}

Lacava, Francesco. Teoria dei campi differenziali ordinati. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975) pp. 322-327. http://gdmltest.u-ga.fr/item/RLINA_1975_8_59_5_322_0/

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