Dedekind completion as a method for constructing new Scott domains
نویسنده
چکیده
Many operations exist for constructing Scott-domains. This paper presents Dedekind completion as a new operation for constructing such domains and outlines an application of the operation. Dedekind complete Scott domains are of particular interest when modeling versions of λ-calculus that allow quantification over sets of arbitrary cardinality. Hence, it is of interest when constructing models of powerful specification languages and when using λ-calculus as a foundation for mathematics.
منابع مشابه
A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS
In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...
متن کاملϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES
The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...
متن کاملA hybrid mean value involving a new Gauss sums and Dedekind sums
In this paper, we introduce a new sum analogous to Gauss sum, then we use the properties of the classical Gauss sums and analytic method to study the hybrid mean value problem involving this new sums and Dedekind sums, and give an interesting identity for it.
متن کاملHausdorff Continuous Solutions of Nonlinear PDEs through the Order Completion Method
It was shown in [13] that very large classes of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. In this paper the regularity of these solutions has significantly been improved by showing that they can in fact be assimilated with Hausdorff continuous functions. The method of solution of PDE...
متن کاملIntegrally Closed Subrings of an Integral Domain
Let D be an integral domain with identity having quotient field K. This paper gives necessary and sufficient conditions on D in order that each integrally closed subring of O should belong to some subclass of the class of integrally closed domains ; some of the subclasses considered are the completely integrally closed domains, Prüfer domains, and Dedekind domains. 1. The class of integrally cl...
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:
- Electr. Notes Theor. Comput. Sci.
دوره 61 شماره
صفحات -
تاریخ انتشار 2002