O-minimal residue fields of o-minimal fields
نویسنده
چکیده
Let R be an o-minimal field with a proper convex subring V . We axiomatize the class of all structures (R, V ) such that kind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in [8] it was shown that certain first order conditions on (R, V ) are sufficient for the o-minimality of kind. Here we prove that these conditions are also necessary.
منابع مشابه
Scanning hall probe microscopy technique for investigation of magnetic properties
Scanning Hall Probe Microscopy (SHPM) is a scanning probe microscopy technique developed to observe and image magnetic fields locally. This method is based on application of the Hall Effect, supplied by a micro hall probe attached to the end of cantilever as a sensor. SHPM provides direct quantitative information on the magnetic state of a material and can also image magnetic induction under a...
متن کاملScanning hall probe microscopy technique for investigation of magnetic properties
Scanning Hall Probe Microscopy (SHPM) is a scanning probe microscopy technique developed to observe and image magnetic fields locally. This method is based on application of the Hall Effect, supplied by a micro hall probe attached to the end of cantilever as a sensor. SHPM provides direct quantitative information on the magnetic state of a material and can also image magnetic induction under a...
متن کاملConcerning the frame of minimal prime ideals of pointfree function rings
Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...
متن کاملA Linear Extension Operator for Whitney Fields on Closed O-minimal Sets
We construct a natural continuous linear extension operator for CWhitney fields (p finite) on closed o-minimal subsets, different from the Whitney’s one [W], based on the geometry of these sets. Introduction. By an o-minimal subset of an Euclidean space R we will mean a subset definable in any o-minimal structure on the ordered field of real numbers R (see [D, DM] for the definition and fundame...
متن کاملPseudo completions and completions in stages of o-minimal structures
For an o-minimal expansion R of a real closed field and a set V of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to V . This is an elementary extension S of R generated by all completions of all the residue fields of the V ∈ V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings u...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 162 شماره
صفحات -
تاریخ انتشار 2011