Let \(E = \lbrace e_1,e_2,\ldots\rbrace\) be a set of individuals.¹ The set of semantic objects \(O\) is the smallest set such that,

1. \(E\subseteq O\);
2. \(\emptyset\in O\);
3. If \(\omega\in O\), then so is \(\lbrace \omega \rbrace\);
4. If \(\omega_1,\omega_2,\ldots,\omega_k\in O\) with \(k > 1\), then so are \(\lbrace\omega_1,\omega_2,\ldots,\omega_k\rbrace\) and \((\omega_1,\omega_2,\ldots,\omega_k)\).

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