A language for topological structures which satisfies a Lindström-theorem
Martin Ziegler · Bulletin of the American Mathematical Society · 1976
I. The language L. Let L2 be the 2-sorted first order language appropriate for structures (?I, a, e), where 21 is a L-structure and a is a set of subsets of A. We call (?I, a) topological if a is a topology. We call a formula of L2 topological if it is built up using the set quantifier 3X only in the form lX(t E X A0), X does not occur positively in 0. (X occurs positively in 0 if a free occurrence of Xin 0 isIinside the scope of an even number of negation symbols. Note. Primitive symbols are A, 1,3x,3X.) L is defined as the set of topological sentences of L2}