Abstract
A monoid $S$ is called an $\omega$-stabilizer (superstabilizer, or stabilizer) if every $S$-polygon has an $\omega$-stable (superstable, or stable) theory. It is proved that every $\omega$-stabilizer is a regular monoid. This confirms the Mustafin–Poizat conjecture and allows us to end up the description of $\omega$-stabilizers.
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