Real closed exponential fields

• Autorzy: Paola D'Aquino , Julia F. Knight , Salma Kuhlmann , Karen Lange
• Języki publikacji: EN

Abstrakty

EN

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 $L_{ω₁^{CK}}$.

Kategorie tematyczne

• 03C60: Model-theoretic algebra
• 03C70: Logic on admissible sets
• 03C57: Effective and recursion-theoretic model theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 219
• Numer: 2
• Strony: 163-190

Daty

wydano

2012

Twórcy

autor

Paola D'Aquino

• Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Viale Lincoln, 5, 81100 Caserta, Italia

autor

Julia F. Knight

• Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, U.S.A.

autor

Salma Kuhlmann

• Fachbereich Mathematik und Statistik, Universität Konstanz, Universitätsstraße 10, 78457 Konstanz, Germany

autor

Karen Lange

• Department of Mathematics, Wellesley College, 106 Central Street, Wellesley, MA 02481, U.S.A.

Identyfikatory

DOI

10.4064/fm219-2-6