منابع مشابه
Creativity and Effective Inseparability
Introduction. Our terminology is from [1]. We consider the collection of all r.e. (recursively enumerable) sets arranged in an effective sequence co1,co2,--•,«;,••• as in the Post-Kleene enumeration, i.e.,cü¡ is the set of all numbers satisfying the condition (3y)T1(i,x, y), where 7\(z,x,y) is the Kleene predicate (cf. [2]). A number set a. is called productive iff there exists a recursive func...
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Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological To-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated ...
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The notions of effective inseparability (for pairs of sets) and of double productivity are defined in [5]. In this paper are considered some extensions of these notions for sequences of sets, and also certain alternative formulations of them in the spirit of Mucnik [3]. Let M be a nonempty recursively enumerable (r.e.) set which will be fixed in each context. By a sequence of sets we mean a seq...
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wK = 1. A necessary condition for separability is derived and is shown to be more sensitive than Bell’s inequality for detecting quantum inseparability. Moreover, collective tests of Bell’s inequality (namely, tests that involve several composite systems simultaneously) may sometimes lead to a violation of Bell’s inequality, even if the latter is satisfied when each composite system is tested s...
متن کاملEeectivizing Inseparability
Smullyan's notion of eeectively inseparable pairs of sets is not the best eeec-tive/constructive analog of Kleene's notion of pairs of sets inseparable by a recursive set. We present a corrected notion of eeectively inseparable pairs of sets, prove a characterization of our notion, and show that the pairs of index sets eeectively inseparable in Smullyan's sense are the same as those eeectively ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1963
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1963-0153554-9