2011/02/21 by Tamás Waldhauser, Waldhauser, Tamás
Computer Science · Mathematics · #06A15 #06E30 #08A40 #94C10 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06A15 #msc:06E30 #msc:08A40 #msc:94C10
paper · pdf · doi:10.48550/arxiv.1102.4355
20 pages, 8 figures
arxiv created 2011/02/21 · openalex publication_date 2011/02/21 · arxiv updated 2011/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification (diagonalization) of variables and under introduction of inessential variables (cylindrification), but they do not necessarily contain projections. Thus the lattice formed by these classes is an extension of the Post lattice. The cardinality of this lattice is continuum, yet it is possible to describe its structure to some extent.