Assignment F
Independence results like this are often established by semantics.
Common Mistakes:
- Few students forgot to show that MP preserves ‘truths’, thus they didn’t state that all theorems are ‘true’.
- Checking all possible valuations of the axiom schemata is crucial in the proof of independence.
Challenge: Prove that Peirce’s Law cannot be deduced by using only axiom schemata and .
Hint: design a three-valued truth assignment and show that any consequence deduced from the axioms will always take value T and Peirce’s Law won’t. You may consider the following table and try to figure out what values x, y and z should take respectively.
| T | T | T |
| T | M | M |
| T | F | F |
| M | T | x |
| M | M | y |
| M | F | z |
| F | T | T |
| F | M | T |
| F | F | T |