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 (Unpublished)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 |
|---|---|
| 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: | Date Event 1993 Completion |
| 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| Status: | Not Peer Reviewed |
| Publication Status: | Unpublished |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 |
| Related URLs: | |
| URI: | https://wrap.warwick.ac.uk/60933/ |
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