Abstract
We consider Kuznetsov’s implicit expressibility and its generalizations, when the implicit expressibility language is augmented with the additional disjunction, implication, and negation logical connectives. It is shown that, for each k ⩾ 3, the implicit extensions in Pk have the cardinality of the continuum. For each k ⩾ 3, we also prove that each of the sets of positively implicit, implicatively implicit, and negatively implicit extensions in Pk contains, respectively, as a proper subset, the set of positively implicit, implicatively implicit, and negatively implicit closed classes. We verify that, for k ⩾ 2, the functions of the set
Originally published in Diskretnaya Matematika (2023) 35, №2, 34–41 (in Russian).
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Artikel in diesem Heft
- Frontmatter
- On the matching arrangement of a graph and properties of its characteristic polynomial
- Realization of even permutations of even degree by products of four involutions without fixed points
- On implicit extensions in many-valued logic
- On radio graceful Hamming graphs of any diameter
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»
- Resistance distance and Kirchhoff index of two kinds of double join operations on graphs
Artikel in diesem Heft
- Frontmatter
- On the matching arrangement of a graph and properties of its characteristic polynomial
- Realization of even permutations of even degree by products of four involutions without fixed points
- On implicit extensions in many-valued logic
- On radio graceful Hamming graphs of any diameter
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»
- Resistance distance and Kirchhoff index of two kinds of double join operations on graphs