Couceiro, Miguel; Haddad, Lucien; Rosenberg, Ivo G. Partial clones containing all Boolean monotone self-dual partial functions. (English) Zbl 1394.08002 J. Mult.-Val. Log. Soft Comput. 27, No. 2-3, 183-192 (2016). Summary: The study of partial clones on \(\mathbf{2}:= \{0, 1\}\) was initiated by R. V. Freivald. In his fundamental paper published in [Sov. Phys., Dokl. 11, 288–289 (1966; Zbl 0149.24405); translation from Dokl. Akad. Nauk SSSR 167, 1249–1250 (1966)], R. V. Frejvald showed, among other things, that the set of all monotone partial functions and the set of all self-dual partial functions are both maximal partial clones on \(\mathbf{2}\). Several papers dealing with intersections of maximal partial clones on 2 have appeared after Freivald work. It is known that there are infinitely many partial clones that contain the set of all monotone selfdual partial functions on \(\mathbf{2}\), and the problem of describing them all was posed by some authors. In this paper we show that the set of partial clones that contain all monotone self-dual partial functions on \(\mathbf{2}\) is of continuum cardinality. Cited in 5 Documents MSC: 08A40 Operations and polynomials in algebraic structures, primal algebras 08A55 Partial algebras Citations:Zbl 0149.24405 PDFBibTeX XMLCite \textit{M. Couceiro} et al., J. Mult.-Val. Log. Soft Comput. 27, No. 2--3, 183--192 (2016; Zbl 1394.08002) Full Text: arXiv Link