The MSOL strengthening of the paper's main theorem

Let the paper's main theorem be the assertion referred to as Theorem $\mathrm{main2}$, concerning the limitations of finite axiomatization in $M$-logic. MSOL strengthening conjecture. Theorem $\mathrm{main2}$ remains valid when the words “$M$-logic” are replaced by “MSOL”. The source gives no further statement of Theorem $\mathrm{main2}$ in the candidate span, so the precise mathematical hypotheses and conclusion require checking in the paper. This is presented as a conjectural strengthening rather than a proved result.