Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
Ressayre considered real closed exponential fields and "exponential" integer parts, i.e., integer parts that respect the exponential function. In 1993, he outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction and then analyze the complexity. Ressayre's construction is canonical once we fix the real closed exponential field R, a residue field section k, and a well ordering ≺ on R. The construction is clearly constructible over these objects. Each step looks effective, but there may be many steps. We produce an example of an exponential field R with a residue field section k and a well ordering ≺ on R such that $D^{c}(R)$ is low and k and ≺ are Δ⁰₃, and Ressayre's construction cannot be completed in $L_{ω₁^{CK}}$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
163-190
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Viale Lincoln, 5, 81100 Caserta, Italia
autor
- Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, U.S.A.
autor
- Fachbereich Mathematik und Statistik, Universität Konstanz, Universitätsstraße 10, 78457 Konstanz, Germany
autor
- Department of Mathematics, Wellesley College, 106 Central Street, Wellesley, MA 02481, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-2-6