Past exam of the logic and set theory course of the University of Oxford / 2007 / A / 2 / ii

Table of contents
- Solution ii

Solution

Choose an auxiliary propositional formula

β

. The two instances of L1 are

α \to (β \to α), α \to (\neg β \to α) .

The instance of L2 with

γ = α

is

(α \to (β \to α)) \to ((α \to (\neg β \to α)) \to (α \to α)) .

Apply modus ponens rule first with the first L1 instance and then with the second. This is an assumption-free logical derivation, so

⊢ α \to α .

In particular no semantic completeness theorem or deduction theorem for propositional logic has been assumed to obtain this identity theorem.

 Ancestors (12)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version