Structure for first order language

Asked Apr 08 '15 at 14:20

Active Apr 08 '15 at 14:37

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Suppose our first order language has two binary function symbols $f,g$ and a constant symbol $c$. Let the structure $\mu$ be defined as $|\mu|=\{ 0,1,2,3 \}$, $f^{\mu}$ is addition modulo $4$, $g^{\mu}$ is multiplication modulo $4$, and $c^{\mu}=3$. Suppose $s(x)=2, s(y)=3$. What is $\bar{s}(fgxyc)$?

I'm having trouble evaluating it. Because I have

$\bar{s}(fgxyc)=f^{\mu}g^{\mu}(\bar{s}(x),\bar{s}(y), \bar{s}(c))$. Then I don't know how to proceed from here as $g^{\mu}$ is $2$-nary function.

By the way, I am reading 'A Mathematical Introduction to Logic' by Enderton, Chapter $2$, section $2.2$ Truth and Models.

asked Apr 08 '15 at 14:20

Idonknow

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Perhaps it should be interpreted as $f\big(g(x,y),c\big)$, see here. – dtldarek Apr 08 '15 at 14:25
@dtldarek: Thanks. It makes sense now. – Idonknow Apr 08 '15 at 14:29
Yes, it is : $\overline s(fgxyc) = f^μ[g^μ(s(x),s(y)),c^μ] = f^μ[g^μ(2,3),3]$. – Mauro ALLEGRANZA Apr 08 '15 at 15:25
It's in so-called Polish notation – abc Apr 08 '15 at 18:38

Structure for first order language

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