Solution
= Solution
A direct case split in the linearly ordered chain verifies types 1 and 2. Peirce's value is $P(a,b)$ from part (a); for $n\ge3$, choose $0<a>b$, obtaining $P(a,b)=a<1$. Thus type 3 need not be $n$-valid.
= Solution
A direct case split in the linearly ordered chain verifies types 1 and 2. Peirce's value is $P(a,b)$ from part (a); for $n\ge3$, choose $0<a>b$, obtaining $P(a,b)=a<1$. Thus type 3 need not be $n$-valid.