Fixed points in \(\mathrm{MS}_n\)-algebras (Q2839875)

An Ockham algebra \((L,f)\) is a bounded distributive lattice \(L\) endowed with a dual endomorphism \(f\). An \(\mathrm{MS}_n\)-algebra is an Ockham algebra that satisfies \(x\wedge f^{2n}(x)=x\). A fixed point of an Ockham algebra \((L,f)\) is an element \(x\in L\) such that \(f(x)=x\). The present paper determines, for each subvariety \(\mathbf V\) of \(\mathbf{MS}_n\), the set of those cardinalities which occur as cardinalities of the sets of fixed points of the countable algebras that generate \(\mathbf V\).