\title {Logic I \\ Lecture 18}

\maketitle

\section{Proofs about Proofs}

\section{Proofs about Proofs}

\section{A ⊨ ⊥}

\section{A ⊨ ⊥}

\section{If (A ⊬ ⊥ entails A ⊭TT ⊥) then (A ⊨TT B entails A ⊢ B) }

\section{If (A ⊬ ⊥ entails A ⊭TT ⊥) then (A ⊨TT B entails A ⊢ B) }

\section{The Essence of the Completeness Theorem}

\emph{Reading:} §8.3

\section{The Essence of the Completeness Theorem}

\section{Lemma for the Completeness Theorem}

\emph{Reading:} §8.3

\section{Lemma for the Completeness Theorem}

\section{Proof of the Completeness Theorem}

\emph{Reading:} §8.3, §17.1, §17.2

\section{Proof of the Completeness Theorem}

\section{Proof of Proposition 4 for the Completeness Theorem}

\emph{Reading:} §15.1, §15.6

\section{Proof of Proposition 4 for the Completeness Theorem}

15.33--15.40 (second edition)

15.33, 15.37--15.39 (second edition)