 Solution

ID: past-exam-of-the-logic-and-set-theory-course-of-the-university-of-oxford/2008/a/1/e/i/solution

p_{i}

is a single symbol of the alphabet. Its only nonempty substring is that symbol itself. Every propositional formula is nonempty, so the only substring that is a logical formula is

p_{i}

. Therefore

Sub (p_{i}) = {p_{i}} .

The subscript is part of the name of an atomic token; it does not introduce additional symbol positions inside the logical variable.

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