A class of \(\Sigma_{3}^{0}\) modular lattices embeddable as principal filters in \({\mathcal L}^*(V_\infty)\)
Let \(V_\infty\) be an effective infinite-dimensional vector space over a computable field, and \({\mathcal L}^*(V_\infty)\) be the lattice of c.e. subspaces of \(V_\infty\) modulo the equivalence relation \(=^*\) (where \(A =^* B\) if the sets \(A\) and \(B\) differ by finitely many elements). The paper establishes certain structural properties of \({\mathcal L}^*(V_\infty)\), which, combined with an earlier result of the author [``Quasimaximality and principal filters isomorphism between \({\mathcal E}^*\) and \({\mathcal L}^*(V_\infty)\)'', Arch. Math. Logic 43, No. 3, 415--424 (2004; Zbl 1059.03040)], lead to a characterization of the principal filters of \({\mathcal L}^*(V_\infty)\).
scientific article; zbMATH DE number 5351802