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Weakly implicatively selective sets of dimension 3

Weakly implicatively selective sets of dimension 3 -- For an rc-place Boolean function , we define a class () of weakly -implicatively selective sets, which are subsets of the set of natural numbers. The dimension of the class () is the number of essential variables of the function . We describe, up to inclusion, all classes () of dimension 2 and 3, excepting one case. This paper can be considered as a continuation of the paper [1] and is close to papers [2, 3]. Let A C = {0. 1,2, . . . } and be an rc-place Boolean function without fictitious variables. For G N, we set = 1 if and je = 0 otherwise. A set A is called weakly -implicatively selective ( -IS) set if there exists an rc-place partial recursive function / such that (V*!,... , We say that / corresponds to A. We set K (ft) = {A C N: A is a -IS set}, and the number n will be referred to as the dimension of the class A Boolean function is admissible if (0, . . . ,0) = 0. It is clear that if is not admissible, then (ft) -- {N}, and this case is of no http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics and Applications de Gruyter

Weakly implicatively selective sets of dimension 3

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0924-9265
eISSN
1569-3929
DOI
10.1515/dma.1999.9.4.395
Publisher site
See Article on Publisher Site

Abstract

-- For an rc-place Boolean function , we define a class () of weakly -implicatively selective sets, which are subsets of the set of natural numbers. The dimension of the class () is the number of essential variables of the function . We describe, up to inclusion, all classes () of dimension 2 and 3, excepting one case. This paper can be considered as a continuation of the paper [1] and is close to papers [2, 3]. Let A C = {0. 1,2, . . . } and be an rc-place Boolean function without fictitious variables. For G N, we set = 1 if and je = 0 otherwise. A set A is called weakly -implicatively selective ( -IS) set if there exists an rc-place partial recursive function / such that (V*!,... , We say that / corresponds to A. We set K (ft) = {A C N: A is a -IS set}, and the number n will be referred to as the dimension of the class A Boolean function is admissible if (0, . . . ,0) = 0. It is clear that if is not admissible, then (ft) -- {N}, and this case is of no

Journal

Discrete Mathematics and Applicationsde Gruyter

Published: Jan 1, 1999

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