The only way I can make sense of the result of the abstract is as follows:

Let $M$ be any nonstandard model of PA (Peano arithmetic), then it is well-known (and first demonstrated by Feferman in [this 1964 paper][1], using an arithmetical adaptation of Cohen forcing), one can build an infinite family $\cal{S}$ of subsets of $M$ such that the structure $(M,S)_{S\in\cal{S}} $ obtained by adding each $S \in \cal{S}$ to $M$ as an extra predicate satisfies the axioms of Peano arithmetic in the extended language (i.e., the language of arithmetic augmented with a distinguished predicate symbol for each $S \in \cal{S}$).

Note that the aforementioned Feferman paper is listed in listed in the references of the paper by Zhang Jinwen.

I should also add that it is also well-known that the family $\mathcal{S}$ above can be arranged to be of power continuum. More information about forcing (of the Cohen and Sacks variety) in arithmetic can be found in Kossak and Schmerl's monograph The Structure of Models of Peano Arithmetic. [1]: http://matwbn.icm.edu.pl/ksiazki/fm/fm56/fm56129.pdf

The only way I can make sense of the result of the abstract is as follows:

Let $M$ be any nonstandard model of PA (Peano arithmetic), then it is well-known (and first demonstrated by Feferman in [this 1964 paper][1], using an arithmetical adaptation of Cohen forcing), one can build an infinite family $\cal{S}$ of subsets of $M$ such that the structure $(M,S)_{S\in\cal{S}} $ obtained by adding each $S \in \cal{S}$ to $M$ as an extra predicate satisfies the axioms of Peano arithmetic in the extended language (i.e., the language of arithmetic augmented with a distinguished predicate symbol for each $S \in \cal{S}$).

Note that the aforementioned Feferman paper is listed in the references of the paper by Zhang Jinwen.

I should also add that it is also well-known that the family $\mathcal{S}$ above can be arranged to be of power continuum. More information about forcing (of the Cohen and Sacks variety) in arithmetic can be found in Kossak and Schmerl's monograph The Structure of Models of Peano Arithmetic.

Postscript. In light of the translation offered by Benjamin Dickman in his answer to the question, along with clarifications made by 喻 良 in his comments on Dickman's answer, it appears that Zhang Jinwen's claim (in his abstract) cannot be interpreted so as to coincide with the well-known result offered in my answer.