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But in Unions NSW, the main judgement held the challenged provisions not only had no legitimate purpose, but seemed to have no purpose at all. The topics must be submitted for feedback to the instructors at the latest on 2 April. Even if you are already familiar with the material, you may wish to look over Chapters 5--8 to familiarize yourself with the notation, definitions, and conventions used here, or at least keep them handy in case you need to check some such point. \end{note} \subsection*{A language for first-order number theory} To keep things as concrete as possible we will work with and in the following language for first-order number theory, mentioned in Example~\ref{e:lan}. \begin{defn} \label{d:LN} \index{$\mathcal{L}_N$} \index{language for first-order number theory} \index{first-order language for number theory} \index{number theory first-order language for} $\mathcal{L}_N$ is the first-order language with the following symbols: \begin{enumerate} \item Parentheses: $($ and $)$ \item Connectives: $\lnot$ and $\to$ \item Quantifier: $\forall$ \item Equality: $=$ \item Variable symbols: $v_0$, $v_2$, $v_3$, \dots \item Constant symbol: $0$ \item $1$-place function symbol: $S$ \item $2$-place function symbols: $+$, $\cdot$, and $E$. \end{enumerate} \end{defn} The non-logical symbols of $\mathcal{L}_N$, $0$, $S$, $+$, $\cdot$, and $E$, are intended to name, respectively, the number zero, and the successor, addition, multiplication, and exponentiation functions on the natural numbers.
Pages: 340
Publisher: Hart Publishing (February 1, 2011)
ISBN: 1849460930
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