“…By [4, Corollary 4.12], we have ๐ท is definable by a positive-existential ๎ธ ring (๐พ)-formula with ๐ quantifiers, that is, a formula which is logically equivalent to โ๐ 1 , โฆ , ๐ ๐ ๐ for some ๎ธ ring (๐พ)formula ๐ built up from atomic ๎ธ ring (๐พ)-formulae using only conjunctions and disjunctions (no negations). By [4,Remark 3.4], this implies ๐ท can be described as in (2) for certain ๐ and ๐ 1 , โฆ , ๐ ๐ , where one may choose ๐ = 1 when ๐พ is not algebraically closed. โก…”