Non-semi-decidability of LEF and isolated groups

Let $\mathcal{G}$ be the space of marked groups and $\mathcal{G}_{WP}$ its subspace of marked groups with solvable word problem. A property is $\Lambda_{WP}$-semi-decidable or $\Lambda_{WP}$-co-semi-decidable according to whether it can be semidecided, respectively, by the word-problem representation or by its complement. LEF groups are groups that are limits of finite groups, and isolated groups are open singleton points of $\mathcal{G}$.

LEF and isolated-groups conjecture. The set of LEF groups is not $\Lambda_{WP}$-co-semi-decidable, and the set of isolated groups is not $\Lambda_{WP}$-semi-decidable.

These are proposed as natural failures of correspondence between topological and arithmetical classifications. The paper gives no proof and contrasts them with pathological counterexamples built using Kolmogorov complexity.