Ordinal definability in the rank hierarchy
نویسندگان
چکیده
منابع مشابه
Turing Definability in the Ershov Hierarchy
We obtain the first nontrivial d.c.e. Turing approximation to the class of computably enumerable (c.e.) degrees. This depends on the following extension of the splitting theorem for the d.c.e. degrees: For any d.c.e. degree a, any c.e. degree b, if b < a, then there are d.c.e. degrees x0,x1 such that b < x0,x1 < a and a = x0 ∨ x1. The construction is unusual in that it is incompatible with uppe...
متن کاملAn ordinal indexed hierarchy of separation properties
We refine and stratify the standard separation properties to produce a descending hierarchy between T3 and T1. The interpolated properties are related to the patch properties and the Vietoris modifications of the parent space.
متن کاملSlicewise Definability in First-Order Logic with Bounded Quantifier Rank
Abstract For every q ∈ N let FOq denote the class of sentences of first-order logic FO of quantifier rank at most q. If a graph property can be defined in FOq, then it can be decided in time O(n). Thus, minimizing q has favorable algorithmic consequences. Many graph properties amount to the existence of a certain set of vertices of size k. Usually this can only be expressed by a sentence of qua...
متن کاملInvariance to ordinal transformations in rank-aware databases
We study influence of ordinal transformations on results of queries in rank-aware databases which derive their operations with ranked relations from totally ordered structures of scores with infima acting as aggregation functions. We introduce notions of ordinal containment and equivalence of ranked relations and prove that infima-based algebraic operations with ranked relations are invariant t...
متن کاملRank of Handelman hierarchy for Max-Cut
We consider a hierarchical relaxation, called Handelman hierarchy, for a class of polynomial optimization problems. We prove that the rank of Handelman hierarchy, if applied to a standard quadratic formulation of Max-Cut, is exactly the same as the number of nodes of the underlying graph. Also we give an error bound for Handelman hierarchy, in terms of its level, applied to the Max-Cut formulat...
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: Annals of Mathematical Logic
سال: 1973
ISSN: 0003-4843
DOI: 10.1016/0003-4843(73)90002-8