Abstract
Functional equations formed for functions of real variables and containing only the functional constants 0, 1, +, and × are considered. The expressive power of the language ℒ of functional equations is studied. It is proved that the language ℒ can be extended to a language with the same class of definable sets by adding a complete system of logical connectives and quantifiers with respect to object variables. The algorithmic unsolvability of the satisfiability problem for ℒ is proved. Some well-known real numbers and continuous functions are defined by means of ℒ.
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