There are four papers by Vladimir Alfeevich Kuznetsov, which discuss the above titled topic:

(1) Some problems in set theory from the standpoint of a formal system G+ of Gentzen type. (Russian) Akad. Nauk Ukrainy Inst. Mat. Preprint 1992, no. 21, 51 pp.

(2) The forcing method from the point of view of a formal system G+ of Gentzen type. (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1991, no. 19, 59 pp.

(3) Classical descriptive set theory from the point of view of the Gentzen-type formal system G+. (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1990, no. 40, 63 pp.

(4) Set theory from the point of view of the Gentzen-type formal system G+. (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1990, no. 13, 63 pp.

The papers are in Russian, and I even could not find any access to them. Also their review in Mathscinet do not say much about the results of the papers.

I wonder to know if someone can explain in some details the results obtained in the above papers, in particular paper no. 2.

 

Also I am interested in finding some reference in English related to the above papers.

Thanks in advance.

Remark. As an example, the review of the second paper in Mathscinet is as follows:

"This paper is devoted to a systematic presentation of the forcing method in a nontraditional focus: we present proofs of theorems in the form of trees of a formal system $G^+$ of Gentzen type in the Zermelo-Fraenkel and Morse axiom systems. The proofs presented contain practically all the nuances of set-theoretic constructions.''

See here for the review of the papers.

There are four papers by Vladimir Alfeevich Kuznetsov, which discuss the above titled topic:

(1) Some problems in set theory from the standpoint of a formal system G+ of Gentzen type. (Russian) Akad. Nauk Ukrainy Inst. Mat. Preprint 1992, no. 21, 51 pp.

(2) The forcing method from the point of view of a formal system G+ of Gentzen type. (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1991, no. 19, 59 pp.

(3) Classical descriptive set theory from the point of view of the Gentzen-type formal system G+. (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1990, no. 40, 63 pp.

(4) Set theory from the point of view of the Gentzen-type formal system G+. (Russian) Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1990, no. 13, 63 pp.

The papers are in Russian, and I even could not find any access to them. Also their review in Mathscinet do not say much about the results of the papers.

I wonder to know if someone can explain in some details the results obtained in the above papers, in particular paper no. 2.

Also I am interested in finding some reference in English related to the above papers.

Thanks in advance.

Remark. As an example, the review of the second paper in Mathscinet is as follows:

"This paper is devoted to a systematic presentation of the forcing method in a nontraditional focus: we present proofs of theorems in the form of trees of a formal system $G^+$ of Gentzen type in the Zermelo-Fraenkel and Morse axiom systems. The proofs presented contain practically all the nuances of set-theoretic constructions.''

See here for the review of the papers.