Dedicated to the Memory of Honored Scientist of Georgia Shalva Pkhakadze (1919-1994)

An honoured scientist, Professor Shalva Pkhakadze was born on 7th April in 1919. He graduated with honours from the faculty of Physics and Mathematics at Ivane Javakhishvili Tbilisi State University in 1941. During the next 10 years, he was busy with teaching at the village schools of Zestafoni district, where he began to study prominent scientific topics of that time.

In 1952 as a result of this abovementiond independent researches, Shalva Pkhakadze was invited in A. Razmadze Mathematical Institute, where after a year - in 1953 he defended his dissertation for candidate of science, and in 1956 he presented for publishing doctoral work "The theory of Lebesgue measure". Because of in A. Razmadze Mathematical Institute publishing processes were stopped for three years he successfully defended the thesis and earned the doctoral degree only in 1959. Pyotr Novikov - a famous Russian mathematician has appreciated this fundamental work by the next: "The extension problem in Measure Theory is one of the fundamental and it is natural that this issue rouses big interest. Despite of the interest, a solution for the problem about extending the Lebesgue’s type measure, was not visible and was not advancing forward. The dissertation under consideration is an important step forward in the above-mentioned direction, moreover, I would say, that it moved theory from the dead point". - Thus, in just four years, Shalva Pkhkadze managed not only to get degrees of candidate and doctor of science, but also gave an important stimulus to one of the very prominent for that time mathematical direction. - This can be considered as an almost unprecedented fact of pushing scientific results forward in a very short time.

From 1960, in parallel to the scientific activities, he actively participates in teaching activities at the university. In 1965 he got the titles of professor, in 1967 - the titeles of honoured scientist.

Despite of his important results in Measure Theory, in years 1967-1969, he changes his scientific domain and begins to study Mathematical Logic. Of course, it was not easy for him to change scientific domain, but considering the necessity of founding and developing in Georgia Mathematical Logic, he decided to make this step. Consequences, in 1969, in the Ilia Vekua Institute of Applied Mathematics, he formed a special department of "Mathematical Logic and Theory of Algorithms", were it was beguan first Georgian researches in these directions. At the same time, he was leading seminars and giving special courses in Mathematical Logic at the Ivane Javakhishvili Tbilisi State University.

Thus, from 1969 - at the second stage of his scientific activities there were done very significant results by Shalva Pkhakadze into directions of Mathematical Logic and Theory of Algorithms. Namely, in his work "One Example of Intuitively Computable and Everywhere Defined Function and Church's Thesis", published in 1984, he described an intuitively computable and everywhere defined function, which, according to his thesis, is not recursive. This work casted doubt on the Church's thesis, which was indubitable for that time. But, nowadays, attitude of researchers towards Church's thesis has radically changed - there are published many papers disclaiming this thesis. This circumstance, and it is veru clear, increases credibility in correctness of the Pkhakadze’s thesis, which, in turn, is opposite thesis of the Church's thesis. However, even renouncement of such an important thesis as Church's thesis, cannot be compared to what Notation Theory gave to Mathematical Logic. Truly, his Notation Theory, which was firstly described in his work "Some Problems of Notation Theory" published in 1977, equippes a classical mathematical formalism with the property of formal development, which, and it is very cleare, had lacking this formalism before. It must be noted as well, that Notation Theory significantly contributed to the development of the theory of the Term Rewriting Systems. At the first stage in the Term Rewriting Systems, it was only possible to compute expressions without bound variables, at the second stage on the basis of Shalva Pkhakadze’s Notation Theory, there was developed the theory of the Higher Order Term Rewriting Systems, which nowadays is a very important part of Term Rewriting Systems. - This is one more very clear confirmation of the high scientific significance of the Notation Theory introduced by Shalva Pkhakadze.

Thus, taking in to accout all abovementiond, we underlien, main result of Shalva Pkhakadze’s non-standard career is a fact that today together with other Georgian mathematical schools, there exists and develops also a Georgian school of the Classical Mathematical Logic the founder of which is he.