6:T1a14,

Theorem 17.2 (Unique language from compatible cuts). Every compatible Boolean cut field determines a unique language $L_C=\{w:C_{|w|,0}(w,\eps)=1\}$ such that $C_{m,n}(u,v)=\mathbf 1[uv\in L_C]$ for every cut. Conversely, every language produces a compatible field.

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