The following result is an approximation to the answer of the question of Kokorin (Logical Notebook, Unsolved Problems of Mathematics, Novosibirsk, 1986, 41pp; in Russian) about decidability of a quantifier-free theory of field of rational numbers. Let Q₀ be a subset of the set of all rational numbers which contains integers 1 and −1. Let be a set containing Q₀ and closed by the functions of addition, subtraction and multiplication. For example coincides with Q₀ if Q₀ is the set of all binary rational numbers or the set of all decimal rational numbers. It is clear that , where Z is the set of all integers and Q is the set of all rational numbers. A negationless theory uses only conjunction and disjunction as logical connectives. Let T be a quantifier-free (universal or free-variable) negationless elementary theory of signature , where Pol is the list of all polynomials with rational coefficients from Q₀ in which exponent of the polynomials and rational coefficients are written in binary number system.

Theorem 1. Theory T is NP-hard and if is everywhere dense then the theory T is decidable by an algorithm which belongs to EXPTIME. The set of all rational numbers or the set of all binary rational numbers may be taken instead of . The quantifier-free negationless theory of the field of rational numbers may be regarded as a base of constructive mathematics (Section Mathematical Logic and Foundations of Mathematics, ICM, Warszawa, 1982, p. 21).