Type Two Cuts, Bad Cuts and Very Bad Cuts
نویسنده
چکیده
Type two cuts, bad cuts and very bad cuts are introduced in [KL] for studying the relationship between Loeb measure and U-topology of a hyper nite time line in an !1-saturated nonstandard universe. The questions concerning the existence of those cuts are asked there. In this paper we answer, fully or partially, some of those questions by showing that: (1) type-two cuts exist, (2) the @1-isomorphism property implies that bad cuts exist, but no bad cuts are very bad. 0 Introduction All nonstandard universes mentioned in this paper are !1-saturated. Given a nonstandard universe V , let N denote the set of all positive integers in V and N denote the set of all standard positive integers. A non-empty initial segment U of N (under the natural order of N) is called a cut if U is closed under addition, i.e. (8x; y 2 U) (x + y 2 U) is true. For example, N is the smallest cut and N is the largest cut. There are several ways of constructing new cuts from given cuts shown in [KL]. For example, if U is a cut and x is an element in N , then the set xU = fy 2 N : (9z 2 U) (y < xz)g is a cut. If the element x is in N r U , then the set x=U = fy 2 N : (8z 2 U) (y < x=z)g is also a cut. Mathematics Subject Classi cation Primary 03H05, 03H15, 03C50 This research was partially supported by NSF postdoctoral fellowship #DMS-9508887.
منابع مشابه
A note on "An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts"
The technique for order of preference by similarity to ideal solution (TOPSIS) is a method based on the ideal solutions in which the most desirable alternative should have the shortest distance from positive ideal solution and the longest distance from negative ideal solution. Depending on type of evaluations or method of ranking, different approaches have been proposing to calculate distances ...
متن کاملA Probabilistic Analysis of the Strength of the Split and Triangle Closures
In this paper we consider a relaxation of the corner polyhedron introduced by Andersen et al., which we denote by RCP. We study the relative strength of the split and triangle cuts of RCP’s. Basu et al. showed examples where the split closure can be arbitrarily worse than the triangle closure under a ‘worst-cost’ type of measure. However, despite experiments carried out by several authors, the ...
متن کاملCharacterization of the split closure via geometric lifting
We analyze split cuts from the perspective of cut generating functions via geometric lifting. We show that α-cuts, a natural higher-dimensional generalization of the k-cuts of Cornuéjols et al., gives all the split cuts for the mixed-integer corner relaxation. As an immediate consequence we obtain that the k-cuts are equivalent to split cuts for the 1-row mixed-integer relaxation. Further, we s...
متن کاملScenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach
The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of ...
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:
- J. Symb. Log.
دوره 62 شماره
صفحات -
تاریخ انتشار 1997