On the locality of arb-invariant first-order formulas with modulo counting quantifiers

Abstract

Abstract. We study Gaifman locality and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MOD p , for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas.

Modulo Counting on Words and Trees

“…A survey of results in first order logic extended with modulo counting quantifiers can be found in [22]. Recent research in this area involves a study of definability of regular languages on words and its connections to algebra [22], [23]; definable languages of (N, +) [19], [14]; equivalences of finite structures [17]; definable tree languages [18], [5]; locality [11], [12]; extensions of Linear Temporal Logic [1], [21], complexity of the model-checking problem [12], [6]. Not much is known about the complexity of the satisfiability problem for this logic.…”