# Tag Info

### Strong Completenss vs Finitely Strong Completenss

The canonical example of this is the logic $L(Q)$ gotten by adding the quantifier $Q\equiv$ "There exist uncountably many" to first-order logic. Improving on earlier work of Vaught, Keisler ...
• 251k

### Proof of the principle of explosion

Re the second point in your question, the proof still holds. We have (1) $P$ and (2) $¬P$ as assumptions. Instead of deriving (3) $P \lor Q$ from (1) by Disjunction introduction (aka: Addition), we ...
• 95.2k
1 vote
Accepted

### How can a problem with cases be represented formally?

Naïm Favier's comment is spot-on. First: A person who always tells the truth is called a "knight". It's quicker to say and to understand "$A$ is a knight" than to say or ...
1 vote

### Meta-logic of Hilbert-style propositional calculus

Basically, we have two methods in logic to specify an axiomatic system: Either we enumerate axioms and inference rules, defining uniform/simultaneous substitution as a syntactic rule or a metatheorem; ...
• 2,521

Only top scored, non community-wiki answers of a minimum length are eligible