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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2023--24--A term}\\[0.2\baselineskip]

\end{center}

\begin{description}
  \item[Course Name]
    Logic

  \item[Course Number]
    \LRE{201‭.1‭.6061}

  \item[Course web page]\mbox{}\\
    \url{https://math.bgu.ac.il//en/teaching/fall2024/courses/logic}

  \item[Lecturer]
    Prof. Assaf Hasson,
    \nolinkurl{<hassonas@bgu.ac.il>},
    Office 204

\item[Office Hours]
  \url{https://math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}

\begin{enumerate}
\item{} Introduction and historical background: the Hilbert-Witehead program, paradoxes in set theory, independence theorems.
\item{} First order logic: formulas, structures truth value of a formula in a model, calculus with and without equality.
\item{} Goedel's Completeness theorem: deduction systems for propositional logic, the completeness theorem for propositional logic and for first order logic. The model existence theorem and the compactness theorem.Applications  and corollaries (Upward Lowenheim-Skolem).
\item{} Goedel's incompleteness theorem: codes, Goedel's fixed point theorem, Tarski's theorem on the non-definability of truth.
\item{} Corollaries of incompleteness, as time allows.
\end{enumerate}


\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}

85\% Take home exam.
10\% HW assignments. 
5\% HW grading (if no grader is found, In case a grader is found these 5\% will be added to the take home exam).




\section*{Course topics}

\begin{itemize}
\item{} An axiom system for predicate calculus and the completeness theorem.
\item{} Introduction to model theory: The compactness Theorem, Skolem--Löwenheim Theorems, elementary substructures.
\item{} Decidability and undecidability of theories, Gödel first Incompleteness Theorem.
\end{itemize}

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