Let \(E\) be an infinite set of individuals.¹ Let \(\top\) and \(\bot\) be two atoms that do not belong in \(E\).

1. \(U_0 = E \cup \lbrace \top,\bot\rbrace\);
2. \(U_{n+1} = U_n \cup \mathcal{P}(U_n) \cup \lbrace\langle x_1, x_2,\ldots,x_k\rangle\mid k \geq 2 \text{ and } x_1, x_2,\ldots,x_k\in U_n \rbrace\);²
3. \(U = \bigcup\limits_{n=0}^{\infty} U_n\).

The set \(U\) is the set of semantic objects.

1. “Individual” is used here in the sense of “indivisible entity”. ↩

2. \(\mathcal{P}\) is the full power set function. ↩