Lob's Theorem

Summary

Lob's Theorem asserts that no formal system T can prove statements of the form "If A is provable in T, then A is true" unless it is also capable of proving A directly. It can be seen as a generalization of Godel's Second Incompleteness Theorem.

Context

This concept has the prerequisites:

Goals

  • Know the statement of Lob's Theorem and why it is significant
  • Show how to derive Godel's Second Incompleteness Theorem as a special case of Lob's Theorem
  • Prove Lob's Theorem

Core resources (read/watch one of the following)

-Free-

Notes on Logic (2013)
Lecture notes for a course on first order logic.
Author: Henry Cohn

-Paid-

See also

-No Additional Notes-