Teoria dei campi differenziali ordinati

Francesco Lacava

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1975)

  • Volume: 59, Issue: 5, page 322-327
  • ISSN: 0392-7881

Abstract

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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.

How to cite

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Lacava, Francesco. "Teoria dei campi differenziali ordinati." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 59.5 (1975): 322-327. <http://eudml.org/doc/290937>.

@article{Lacava1975,
author = {Lacava, Francesco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {11},
number = {5},
pages = {322-327},
publisher = {Accademia Nazionale dei Lincei},
title = {Teoria dei campi differenziali ordinati},
url = {http://eudml.org/doc/290937},
volume = {59},
year = {1975},
}

TY - JOUR
AU - Lacava, Francesco
TI - Teoria dei campi differenziali ordinati
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1975/11//
PB - Accademia Nazionale dei Lincei
VL - 59
IS - 5
SP - 322
EP - 327
LA - ita
UR - http://eudml.org/doc/290937
ER -

References

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