Geodesic
Monoids All Polygons Over Which Are $\omega$-Stable: Proof of the Mustafin – Poizat Conjecture
Algebra i logika, Tome 41 (2002) no. 2, pp. 223-227

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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.
Keywords: monoid, regular monoid, $\omega$-stabilizer, $\omega$-stable theory. 
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     author = {A. A. Stepanova},
     title = {Monoids {All} {Polygons} {Over} {Which} {Are} $\omega${-Stable:} {Proof} of the {Mustafin~{\textendash}} {Poizat} {Conjecture}},
     journal = {Algebra i logika},
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     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_2_a6/}
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A. A. Stepanova. Monoids All Polygons Over Which Are $\omega$-Stable: Proof of the Mustafin – Poizat Conjecture. Algebra i logika, Tome 41 (2002) no. 2, pp. 223-227. http://geodesic.mathdoc.fr/item/AL_2002_41_2_a6/