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Purpose

On the basis of previous work, the authors aim to further study the problem of infinity existing in between predicates and sets.

Design/methodology/approach

A conceptual approach is taken in the paper.

Findings

The authors modify the conventional rule of thinking that each predicate determines a unique set, and establish a principle regarding the relationship between predicates and sets. Then, the authors study the structures of actually infinite, rigid sets.

Originality/value

The structure of actually infinite sets is detailed.

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