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@ -9,7 +9,7 @@
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\begin{enumerate}[(a)]
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\begin{enumerate}[(a)]
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\item $0$ is an ordinal, and if $\alpha$ is
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\item $0$ is an ordinal, and if $\alpha$ is
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an ordinal, so is $\alpha + 1$.
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an ordinal, so is $\alpha + 1$.
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\item If $\alpha$ is an ordinal and $x \in a$,
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\item If $\alpha$ is an ordinal and $x \in \alpha$,
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then $x$ is an ordinal.
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then $x$ is an ordinal.
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\item If $\alpha, \beta$ are ordinals
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\item If $\alpha, \beta$ are ordinals
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and $\alpha \subseteq \beta$,
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and $\alpha \subseteq \beta$,
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@ -54,7 +54,7 @@ An alternative way of formulating this is
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Let $D$ be a class of triples
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Let $D$ be a class of triples
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such that for all $u,x$ there is exactly
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such that for all $u,x$ there is exactly
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one $y$ with $(u,x,y) \in D$
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one $y$ with $(u,x,y) \in D$
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(basicalls $(u,x) \mapsto y$ is a function).
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(basically $(u,x) \mapsto y$ is a function).
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Then there is a unique function $f$ on $A$
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Then there is a unique function $f$ on $A$
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such that for all $x \in A$,
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such that for all $x \in A$,
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@ -158,7 +158,7 @@ This $F$ is called the \vocab{rank function} for $(A, R)$.
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\]
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\]
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and
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and
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\[
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\[
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\rk_R \rank(R) \coloneqq \ran(F).
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\rank(R) \coloneqq \ran(F).
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\]
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\]
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In the special case that $R$ is a linear order on $A$,
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In the special case that $R$ is a linear order on $A$,
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