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\title{5.2-5.5 Questions}
\author{Andrew Lounsbury}
\date{March 25, 2020}
\maketitle

\section{5.2}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
I didn't mark any questions for section 5.2. 

\section{5.3}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{enumerate}
    \item[p. 120]
    This is more of a comment, but $N \vdash \fa y[\phi(\ol{a},y) \leftrightarrow y = \ol{b}]$ seems to me a bit reminiscent of well-definedness for functions. If $N$ provides a deduction for $\phi(\ol{a}, y)$ for some $\Ell_{NT}$-term $\ol{a}$ and some $y$, then $y$ must also be some $\Ell_{NT}$-term $\ol{b}$. Otherwise, the formula $\phi(\ol{a},y)$ isn't really saying anything, much in the same way that a function that isn't well-defined can be somewhat nonsensical. (right?)

    \item[p.120]
    In Definitions 5.3.1 through 5.3.4, they say representable \textbf{(in $\mathbf{N}$)}, but they don't do this through the rest of the chapter. I'm assuming that's because they implicitly mean ``in $N$'' wherever it might be implied, but might it be because we could speak of representable/definable sets/functions in sets of axioms other than $N$? 

    \item[p.120, Def. 5.3.1]
    So, for example, $\phi:\equiv (\fa x)x = x$ represents $A = \N$ (or any other $A$), which means all underlying sets are representable. (right? Or does $\phi$ need to be a $\Delta$-formula, specifically?)

    \item[p.121, Def. 5.3.4]
    Here they seem to say that a function is a subset. Do they mean to say ``Notice that a total function is representable if and only if it\textit{'s codomain}(?) is a representable subset of $\N^{k+1}$.''

    \item[p.121 Def 5.3.5]
    Why do they say ``(possibly)''? This is somewhat confusing. 

\end{enumerate}

\section{5.4}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
I didn't mark any questions for section 5.4. 

\section{5.5}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{enumerate}
    \item[p.135, Table 5.1]
    Is there any reason for using these numbers in particular? For instance, would it matter at all if ``$)$'' had the Symbol Number 23 while ``$($'' had the Symbol Number 21? 

\end{enumerate}
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