On representing concepts in finite models

We present a, method of transferring Tarski's technique of classifying finite order concepts by means of truth-definitions into finite model theory. The other considered question is the problem of representability relations on words or natural numbers in finite models. We prove that relations representable in finite models are exactly those which are of degree less than or equal to 0'. Finally, we consider theories of sufficiently large finite models. For a given theory T we define sl(T) as the set of all sentences true in almost all finite models for T. For theories of sufficiently large models our version of Tarski's technique becomes practically the same as the classical one. We investigate also degrees of undecidability for theories of sufficiently large finite models. We prove for some special theory ST that its degree is stronger than 0' but still not more than Sigma (0)(2).