This is an episode in a series on mathematical logic approached with some rigour. Here, we will be closely following the book by Peter B. Andrews: An Introduction To Mathematical Logic and Type Theory. In this episode, we will:
- Learn about well-formed formulas.
- Show the equivalence of the well-formed formula definition to that of a formation sequence on a formula.
- Revisit the principle of mathematical induction and complete induction on the natural numbers.
- Learn the principle of induction on the construction of a well-formed formula.
- Learn about substitutions in the context of propositional logic. And use this idea to derive one of De Morgan’s Laws.
The only knowledge this post will assume is a basic knowledge in set theory.
(The Prelude) Before we start with logic, let’s revise two ideas which may serve to be important later on. If one is familiar with the principle of mathematical induction and strong induction, one may skip this.…