transitive closure

The transitive closure of a set $X$ is the smallest transitive set $\\operatorname{tc}(X)$ such that $X\\subseteq\\operatorname{tc}(X)$ .

The transitive closure of a set can be constructed as follows:

Define a function $f$ on $\\omega$ by $f(0)=X$ and $f(n+1)=\\bigcup f(n)$

\\operatorname{tc}(X)=\\bigcup_{n<\\omega}f(n)

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