Continuing this process one clearly gets Combinatorial Hierarchy. The somewhat mysterious feature is the dropping of one statement. There is second construction which is purely set theoretical and gives a natural explanation for the dropping of one statement. There are 3 of them if the physically nonrealizable empty set is excluded. By continuing the process one finds that the numbers of the Combinatorial Hierarchy result.
Boolean statement is the basic reason for dropping it from consideration.
The numbers of the Combinatorial Hierarchy have some properties, which suggest that they are very closely related to the Genetic Code. Therefore the set of the Boolean statements has also interpretation as a simplified model for arithmetics and the arithemetic abilities of the intelligent system grow gradually in transitions from level to metalevel. The model of the Genetic Code Previous observations suggest a general model for Genetic Code. The prediction that at most 6 DNAs correspond to given amino acid is consistent with Cenetic Code. The interpretation of the aminoacid type statements is as general axioms and DNA type statements are regarded as special cases of these axioms.