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Prove the following theorems: Show that if $\mathscr{M}$ is a model of $Q_0$ with exactly $n$ individuals (members of $\mathscr{D}), \mathscr{M} \vDash \bar{n}=Q_{\text {o(o)(or) }}\left[\lambda x_1 T_{\mathrm{o}}\right]$ and $\mathscr{M} \vDash \bar{m}=\left[\lambda p_{o t} F_{\mathrm{o}}\right]$ for each integer $m>n .(\bar{m}$ is defined on p. 209.)

   Prove the following theorems:
Show that if $\mathscr{M}$ is a model of $Q_0$ with exactly $n$ individuals (members of $\mathscr{D}), \mathscr{M} \vDash \bar{n}=Q_{\text {o(o)(or) }}\left[\lambda x_1 T_{\mathrm{o}}\right]$ and $\mathscr{M} \vDash \bar{m}=\left[\lambda p_{o t} F_{\mathrm{o}}\right]$ for each integer $m>n .(\bar{m}$ is defined on p. 209.)

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An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Computer Science & Applied Mathematics)

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Computer Science & Applied Mathematics)

Peter B. Andrews 1st Edition

Chapter 6, Problem 10

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- $\mathscr{M}$ is a model of $Q_0$, a basic theory of quantification, which includes a domain $\mathscr{D}$ with exactly $n$ individuals. - $\mathscr{M} \vDash \bar{n}=Q_{\text{o(o)(or)}}\left[\lambda x_1 T_{\mathrm{o}}\right]$ means that in the model Show more…

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Prove the following theorems: Show that if $\mathscr{M}$ is a model of $Q_0$ with exactly $n$ individuals (members of $\mathscr{D}), \mathscr{M} \vDash \bar{n}=Q_{\text {o(o)(or) }}\left[\lambda x_1 T_{\mathrm{o}}\right]$ and $\mathscr{M} \vDash \bar{m}=\left[\lambda p_{o t} F_{\mathrm{o}}\right]$ for each integer $m>n .(\bar{m}$ is defined on p. 209.)

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