The paper treats of some consequences of the model-theoretic version of Gabrielov's complement theorem from [11], which asserts that the theories T[sub an] (introduced in [11] and T'[sub an] (defined herein) are model-complete. The theory T'[sub an] is a universal modification of T[sub an] in the language L'[sub an] of ordered rings expanded by the symbols of restricted analytic functions, arithmetic roots and multiplicative inverse l/x. We give a short proof of the curve selecting lemma, and next we demonstrate how quantifier elimination, within the structure R[sub an] expanded by multiplicative inverse 1/x (a result due to Denef-van den Dries [4], can be obtained from the complement theorem through a general method of logic. Also presented is an application to definability problems ; namely, a piecewise description of a subanalytic function by restricted analytic functions, arithmetic roots and l/x.
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This paper deals with an axiomatic theory T[sub an] and the expansion R[sub an] of the ordered field of reals, formed by attaching the restricted analytic functions. We show that the theory T[sub an] is model-complete, which may be regarded as a version of Gabrielov's complement theorem. Our proof is based on Robinson's test and it does not involve a partition technique. An immediate corollary is that T[sub an] coincides with the semantic theory Th(R[sub an]) of all sentences true in the structure R[sub an].
W pracy przedstawiono metodologię modelowania stanów świata i akcji elementarnych agentów za pomocą języka logiki pierwszego rzędu. Podano formalną definicje współbieżności akcji i sformułowano kryterium jej efektywności.
EN
This paper presents a methodology for modelling the world states and the agent's actions by using first-order predicate language. A syntactic condition for concurrent actions is formulated. It is shown when this condition is effective.
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