The intrinsic enumerability of linear orders (Q2714036)

A model \(M\) is called intrinsically enumerable if there exists a mapping \(\nu\:\omega\rightarrow {\mathfrak M}\) which is \(\Sigma\)-definable over \(\mathbb {HF}({\mathfrak M})\). The main result asserts that every infinite linear ordering is not intrinsically enumerable. Some criteria are proven for the existential equivalence and inclusions between existential theories of models of the kind \(\langle{\mathbb {HF}}({\mathfrak M}),a\rangle\).