How I can calculate the Morley rank of the type $x = x$ in the theory $ACF_{0}$?
2026-04-04 14:40:30.1775313630
Calculate rank of Morley in $ACF_{0}$
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It all comes down to quantifier elimination, which tells us that every formula is a Boolean combination of polynomial equalities. In a single variable, a polynomial can have only finitely many solutions. Therefore, any formula in a single variable has either finitely or cofinitely many solutions. That means that the Morley rank is no more than one. Since there are infinitely many solutions to $x=x$, the Morley rank is exactly one.