Approximating formulae

The notion of a approximating formula is introduced. Links of approximating formulae and their spectra for pseudofiniteness are studied. Semilattices, lattices, and Boolean algebras related to approximating formulae are found. Rank values of approximating formulae are studied. Relations between approximating formulae and positive, negative, $\forall$-formulae, $\exists$-formulae, $\exists\forall$-formulae, $\forall\exists$-formulae are considered. Families of consistent formulae are considered and their approximability is characterized. The notion of totally approximating sentence is introduced and families of these sentences are characterized in terms of cardinalities of models and cardinalities of signatures.