Partial algebras—survey of a unifying approach towards a two-valued model theory for partial algebras

Abstract

In this survey, with no proofs included, we collect some material scattered through recent papers and a planned monograph, which shows that partial algebras do have a two-valued first order model theory which is simpler and nicer than one might have expected it to be. In section 1 we comment and present some basic definitions. In section 2 a correct and complete two-valued first order logic is developed. In section 3 the three main concepts of “varieties” are presented, while sections 4 and 5 contain some additional axiomatizability results and some applications, respectively. Section 6 contains some additional remarks.