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

Peter B. Andrews

Chapter 7

Incompleteness and Undecidability - all with Video Answers

Educators


Section 1

Gödel Numbering

03:38

Problem 1

Show that Axiom ${ }^{4 s} \in \mathscr{P} \mathscr{R} \mathscr{R}$.

Geno Ellis
Geno Ellis
Numerade Educator
00:59

Problem 2

Construct an example of the test the king might have given the scholars in the parable above, make reasonable assumptions about the computational methods used by the scholars and their rates of work, and compute the time they would actually take to complete the test.

Maxime Rossetti
Maxime Rossetti
Numerade Educator

Problem 3

A set of natural numbers is said to be recursively enumerable (r.e.) iff it is empty or is the range of a recursive function, and a set $\mathscr{S}$ of formulas is said to be recursively enumerable iff $\{$ "A" $\mid \mathbf{A} \in \mathscr{S}\}$ is a recursively enumerable set of numbers. Prove that if $\mathscr{A}$ is any recursively axiomatized extension of $Q_0$, then the set of theorems of $\mathscr{A}$ is recursively enumerable.

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