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rzach merged 1 commit into from
Nov 12, 2025
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Update replacement.tex #412

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5 changes: 3 additions & 2 deletions content/set-theory/ordinals/replacement.tex
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Expand Up @@ -38,7 +38,7 @@

On first encounter, however, this is quite a tangled formula. The
following quick consequence of Replacement probably gives a
\emph{clearer} expression to the intuitive idea we are working with:
\emph{clearer} expression to the intuitive idea we are working with:\footnote{A term is an expression which picks out exactly one object (on any completion of its free variables). For example, ``$\emptyset$'' is a term which picks out the empty set; ``$\{x\}$'' is a term which picks out $x$'s singleton (whatever $x$ might be); ``$x \cup y$'' is a term which picks out the union of $x$ and $y$ (whatever they might be).}

\begin{cor}
For any term $\tau(x)$, and any set $A$, this set exists:
Expand Down Expand Up @@ -69,4 +69,5 @@
f(x)}$.} Replacement, by contrast, is a \emph{powerful} addition to
our axioms, as we will see in \olref[sth][replacement][]{chap}.

\end{document}

\end{document}