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Fix grammatical error in mathematical statement #32

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Fix grammatical error in mathematical statement #32

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2 changes: 1 addition & 1 deletion lection-10.tex
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Expand Up @@ -74,7 +74,7 @@
Очевидно, что $\text{Д}_\mathcal{S} = \text{И}_\mathcal{S} = \text{И}_\text{ФА}$.
То есть $\text{И}_\text{ФА}$ невыразимо в $\mathcal{S}$.

Пусть $\varphi$ таково, что $\llbracket\varphi(\overline{x})\rrbracket = \text{И}$ при $x \in \text{И}_\text{ФА}$.
Пусть $\varphi$ такова, что $\llbracket\varphi(\overline{x})\rrbracket = \text{И}$ при $x \in \text{И}_\text{ФА}$.
Тогда $\vdash\varphi(\overline{x})$, если $x \in \text{И}_\text{ФА}$ и $\vdash\neg\varphi(\overline{x})$, если $x \notin\text{И}_\text{ФА}$.

Тогда $\text{И}_\text{ФА}$ выразимо в $\mathcal{S}$. Противоречие.
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