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\begin{document}

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\hfill March 10, 2003

\begin{center}
\textbf{Errata (comments; fix-up of typos and errors) to}
\end{center}

\noindent
Krzysztof Ciesielski,
{\em Set Theory for the Working Mathematician},

\noindent London Math Society Student Texts {\bf 39},
Cambridge University Press, 1997.

\bigskip

\noindent ($n^i$ means page $n$ line $i$ from the top;
$n_i$ means page $n$ line $i$ from the bottom.)




\bigskip



\begin{description}
\item{$7^1$ --} ``distinguish'' should be ``distinguished.''

\item{p. 43, Ex. 7 --} Solution to this exercise requires Theorem 4.3.2, 
                       from latter Section 4.3. 

\item{$62^7$ --} Displayed statement requires explanation something like:
\begin{quote}
Indeed, if $f$ is a bijection between $\beta$ and $|\beta|$
then $f\restriction \alpha$ is a bijection 
between $\alpha$ and $f[\alpha]$. So 
$\alpha\approx f[\alpha]\approx {\rm Otp}(f[\alpha])$ and so
$|\alpha|=|f[\alpha]|=|{\rm Otp}(f[\alpha])|\leq {\rm Otp}(f[\alpha])\leq|\beta|$,
where the last inequality follows from Corollary~4.2.6
as $f[\alpha]\subset|\beta|$. 
\end{quote}



\item{$67_{7-12}$ --} The comment ``In fact, \ldots of choice'' is false!
                      Remove it all together.
         

\item{$95_{4-9}$ --} The proof of 
                 $\Sigma^0_\beta\subset\Sigma^0_\alpha$ and 
                 $\Pi^0_\beta\subset\Pi^0_\alpha$ does not use induction.  

\item{p. 97, Ex. 5 --} Remove it. Requires more involved technique.  

\item{p. 110, Ex. 1 --} May be too easy: if $h$ is a function from
     Ex. 1 Sec. 7.1 and $f$ is as in the exercise then
     $g=[h\restriction(\real\setminus C)]\cup f$ is as required. 

\item{p. 111, Ex. 4 --}  Too easy. Just take 
            $X=\real\setminus\rational$ and $Y$ -- the Cantor set. 

\item{p. 111, Ex. 5 --}  Replace 
          ``for every continuous function $g\colon\real\to\real$
      the set $\{x\in\real\colon f(x)=g(x)\}$ has cardinality 
      less than $\continuum$'' with ``$f\restriction X$ is discontinuous
      for every $X\in[\real]^\continuum$.''

\item{p. 154, Ex. 6 and 7 --}  Both statements are false. 
In each of these exercises replace 
``Show that for every family 
$\A$ of countable subsets of $\kappa$ such that $|\A|<\continuum$''
with
\begin{quote}
Let $\A$ be a family of countable subsets of $\kappa$ such that 
the set $\{A\in\A\colon |A\cap C|=\omega\}$ is at most countable for every
countable set $C$. Show that if 
$|\A|<\continuum$ then 
\end{quote}


\item{$165_{13}$ --} Replace 
``$\min\{\beta\colon y\in R(\beta+1)\}$'' with 
 ``$\min\{\beta\colon y\in R(\beta)\}$.''

\item{$179_6$ --} Replace 
``$F(x)=\{y\in Y\colon \exists p^y\in\poset\;(\la\widehat{\la
x,y\ra},p^y\ra\in\tau)\}$''
with 
 ``$F(x)=\{y\in Y\colon \exists p^y\in\poset\;
\mbox{ compatible with $p_0$ such that } 
 \la\widehat{\la x,y\ra},p^y\ra\in\tau\}$.''

\item{$179_2$ --} Replace 
``then $p=p^y\leq p_0$''
with 
 ``then there exists a $p$ extending $p^y$ and $p_0$.''


\end{description}








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