TL;DR
This paper investigates the statistical mechanics properties of finite pure sets, analyzing their growth, correlations, and limiting behaviors as the number of generations increases.
Contribution
It introduces a novel perspective by applying statistical mechanics to study the structure and asymptotic properties of finite pure sets.
Findings
Derived correlations for chains of various lengths.
Established limiting laws for large numbers of generations.
Provided insights into the growth dynamics of pure sets.
Abstract
We study from a statistical mechanics viewpoint some of the simplest mathematical objects, finite pure sets. Starting from the empty set, new generations are produced step by step, sets of the next generation being those whose elements are the sets of the current generation. We compute in particular correlations and limiting laws for chains of various lengths for the membership relation when the number of generations becomes large.
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