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Prove the following theorems in $\mathscr{N}$ : Add rules of inference for $=$ to $\mathscr{N}$, and prove that the resulting system is sound and complete in the sense of 2609 and 2612.

   Prove the following theorems in $\mathscr{N}$ :
Add rules of inference for $=$ to $\mathscr{N}$, and prove that the resulting system is sound and complete in the sense of 2609 and 2612.

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 3, Problem 6

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$\mathscr{N}$ is a formal system for number theory, typically including axioms and rules of inference for arithmetic operations and quantifiers. To add rules of inference for equality, we include: - Reflexivity: For any term $t$, $t = t$. - Symmetry: If $t_1 = Show more…

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Prove the following theorems in $\mathscr{N}$ : Add rules of inference for $=$ to $\mathscr{N}$, and prove that the resulting system is sound and complete in the sense of 2609 and 2612.

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