DOES P(ω)/fin KNOW ITS RIGHT HAND FROM ITS LEFT?

The paper proves that under CH the shift σ and its inverse σ−1 on P(ω)/fin (equivalently on ω*) are conjugate, via an ω1-stage back-and-forth that crucially uses a Lifting Lemma requiring that the image be an elementary substructure; this is the only use of CH and is spelled out in the introduction and Section 6 (main theorem and role of CH) and in Lemma 6.2 (the Lifting Lemma) . The paper also shows that the general lifting problem is not always solvable, so one must maintain elementarity to avoid bad instances (Section 5 and Theorem 8.8’s finitary criterion) . The model’s outline assumes a blanket “α‑reversing extension lemma for countable subalgebras” and runs a back‑and‑forth without preserving elementarity; this contradicts the paper’s explicit counterexamples and omits the key elementarity invariant used in the paper’s recursion (see the successor-step schematics in Section 6) . Stone duality and the basic setup are aligned with the paper’s framework, but the model’s proof lacks the necessary hypotheses and therefore does not establish the theorem .