Two-Variable Ehrenfeucht-Fraisse Games over Omega-Terms

Fragments of first-order logic over words can often be characterized in terms of finite monoids, and identities of omega-terms are an effective mechanism for specifying classes of monoids. Huschenbett and the first author have shown how to use infinite Ehrenfeucht-Fraisse games on linear orders for showing that some given fragment satisfies an identity of omega-terms (STACS 2014). After revisiting this result, we show that for two-variable logic one can use simpler linear orders.