We show that the complement of a subannlytic set deiinod by real analytic functions from'any subalgebro closed under differentiation is a subaii-alytic set defined by the functions from the some subalgebra. This result has an equivalent formulation in logic: Consider an'expression built from functions 4 ' as above using equalities and inequalities as well as existential and universal quantifiers. Such an expression is equivalent to an existential expression in-volving functions from the same class, provided that the variables approach neither infinity nor the boundary of the domain.
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