# achievements and results

*Basic research areas and the most important results of the school:*

The main focus of research is eksplikatyvne school programming – theory descriptive and declarative programming alhebroyidiv (algebraic structures, which is nominally adequate models and data structures, programs and facilities construction programs). For those structures solved the problem of existence, uniqueness and effective task that lays the foundation for a new direction of science – prohramolohiyi – science programs and logic programming. In this line could give a complete solution set of problems that are fundamental to the ways of further development of science, namely:

- Cleenee the problem of axiomatization of regular and kvazirehulyarnyh algebras;
- problem-Chorcha Katlenda of completeness calculated integer functions and similar problems Tarski and Maltsev for rational functions, vocabulary and meaning of the argument;
- problem of completeness for classes of functions and calculated compositions;
- problem specification manipulation actions in databases and completeness of the class of functions – functions that store referents;
- problem of building research and semantically oriented composite first-order logic of partial functions;
- problem and complete the task of natural SQL-like languages.