We prove completeness of the natural deduction proof calculus for propositional logic.
00:00 Introduction
02:12 Definition: reduced LP
03:13 Definition: Syntactic consistency
05:37 Lemma: If every syntactically consistent set has a model, then ND is complete.
12:48 Definition: Hintikka sets
16:38 Lemma: Every Hintikka set has a model
33:35 Lemma: Every syntactically consistent set can be extended to a Hintikka set
34:16 Claim: Enumerating rLP formulas
39:46 Constructing the extension
46:56 Claim: Delta is syntactically consistent
1:06:15 Claim: Delta is a Hintikka set
1:15:37 Completeness Theorem
The playlist for the course can be found here: https://www.youtube.com/watch?v=0HImO-me_sg
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