Intersections of Real Closed Fields
نویسندگان
چکیده
منابع مشابه
Intersections of Real Closed Fields
1. In this paper we wish to study fields which can be written as intersections of real closed fields. Several more restrictive classes of fields have received careful study (real closed fields by Artin and Schreier, hereditarily euclidean fields by Prestel and Ziegler [8], hereditarily Pythagorean fields by Becker [1]), with this more general class of fields sometimes mentioned in passing. We s...
متن کاملReal closed exponential fields
In an extended abstract [20], Ressayre considered real closed exponential fields and integer parts that respect the exponential function. 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. The construction becomes canonical once we fix the real closed exponential field R, a re...
متن کاملQuite Complete Real Closed Fields
We prove that any ordered field can be extended to one for which every decreasing sequence of bounded closed intervals, of any length, has a nonempty intersection; equivalently, there are no Dedekind cuts with equal cofinality from both sides. Here we strengthes the results from the published version.
متن کاملDegree Spectra of Real Closed Fields
Several researchers have recently established that for every Turing degree c, the real closed field of all c-computable real numbers has spectrum {d : d′ ≥ c′′}. We investigate the spectra of real closed fields further, focusing first on subfields of the field R0 of computable real numbers, then on archimedean real closed fields more generally, and finally on nonarchimedean real closed fields. ...
متن کاملAn Intuitionistic Axiomatisation of Real Closed Fields
We give an intuitionistic axiomatisation of real closed fields, which has the constructive reals as a model. The main result is that this axiomatisation together with just the decidability of the order relation gives the classical theory of real closed fields. To establish this we rely on the quantifier elimination theorem for real closed fields due to Tarski, and a conservation theorem of clas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1980
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1980-034-2