Boolean topological graphs of semigroups: the lack of first-order axiomatization

• DOI: 10.1007/s00233-014-9582-3
• Publication Date: 2014-02-12T09:56:38Z
• Authors: Michał M. Stronko...; Belinda Trotta
• Keywords: Complete Boolean algebra

The graph of an algebra A is the relational structure G(A) in which relations are graphs basic operations A. For a class 𝒞 algebras let G(𝒞)={G(A)∣A∈𝒞}. Assume that semigroups possessing nontrivial member with neutral element and ℋ be universal Horn generated by G(𝒞). We prove Boolean core ℋ, i.e., topological prevariety finite members equipped discrete topology, does not admit first-order axiomatization relative to all structures language ℋ. derive analogous results when monoids or groups member.