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Consistency of natural relations on sets
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Koizumi, Hirotaka, Maruoka, Akira and Paterson, Michael S. (1993) Consistency of natural relations on sets. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)
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Abstract
Five natural relations for sets, such as inclusion, disjointness, intersection, etc., are introduced in terms of the emptiness of the subsets defined by Boolean combinations of the sets. Let N denote {1,2,...,n} and (N 2) denote {(i,j) | i,j in N and i < j}. A function mu on (N 2) specifies one of these relations for each pair of indices. Then mu is said to be "consistent on" M, a subset of N, if and only if there exists a collection of sets corresponding to indices in M such that the relations specified by mu hold between each associated pair of the sets. In this paper it is proved that if mu is consistent on all subsets of N of size three then mu is consistent on N. Furthermore, conditions that make mu consistent on a subset of size three are given explicitly.
Item Type: | Report | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Library of Congress Subject Headings (LCSH): | Set theory | ||||
Series Name: | Department of Computer Science research report | ||||
Publisher: | University of Warwick. Department of Computer Science | ||||
Official Date: | 1993 | ||||
Dates: |
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Number: | Number 253 | ||||
Number of Pages: | 10 | ||||
DOI: | CS-RR-253 | ||||
Institution: | University of Warwick | ||||
Theses Department: | Department of Computer Science | ||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Funder: | British Council | ||||
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