Course material for Computability and Definability

Previous update: March 30, 2001
Last update: March 31, 2001
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To learn the material DO the recommended homework !

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Slides for Computability and Definability

  1. Lecture of 8.3.2001 , (29 slides, final) (4 slides/page)

    Introduction to the course, the overall picture.

  2. Lecture of 15.3.2001 , (19 slides, final) (4 slides/page)

    The notion of definability in First Order and Second Order Logic. Many examples.

  3. Lecture of 22.3.2001 , (21 slides, final) (4 slides/page)

    How to prove non-definability. Compactness, Ehrenfeucht-Fraisse games. Many examples.

  4. Lecture of 29.3.2001 , (27 slides, final) (4 slides/page)

    Proving the Ehrenfeucht-Fraisse Theorem.

  5. Lecture of 5.4.2001 (25 slides, NEW final) (4 slides/page)

    The Buechi-Trakhtenbrot Theorem. Pumping lemmas. Non-definability in MSOL.

    Chag Sameach UPessach kasher

  6. Lecture of 19.4.2001 (23 slides, ALMOST final) (4 slides/page)

    The complexity of the satisfaction relation for SOL and its fragments. The polynomial hierarchy and its lower complexity classes. Horn clauses and Existential Second Order Horn formulas.

    Yom Atzmaut Sameach

  7. Lecture of 3.5.2001 (30 slides, ALMOST final) (4 slides/page)

    Presentation of projects

    Translation schemes, the induced maps, transductions and reductions. Fundamental property of translation schemes. Many examples. Complexity of translation schemes. Applications to non-definability.

  8. Lectures 8-11 (50 slides, Almost final) (4 slides/page)

    Model checking in infinite structures. What is the problem? Theories as sets of true sentences in an (infinite) structure. Decidable theories, undecidable theories. using translation schemes to show decidability and undecidability of theories.

    • 10.5.2001: Slides 1-16
    • 17.5.2001: Slides 17-31
    • 24.5.2001: Slides 32-37, 47-53

    Chag Shavuoth Sameach

    • 31.5.2001: Reading assignment
      Chapter 6 of Finite Model Theory by H.-D. Ebbinghaus and J. Flum, Springer 1995.

  9. Lecture of 7.6.2001 (26 slides) (4 slides/page)
    Tarski Centenary Lecture.
    Algorithmic Uses of the Feferman Vaught Theorem
    The Feferman Vaught Theorem. MSOL-inductiv classes of graphs. Representation of structures as parse terms of inductive classes. Polynomial time algorithms for MSOL-definable properties on inductive classes.

  10. Lecture of 14.5.2001 (xx slides, in preparation) (4 slides/page)

  11. Lecture of 21.5.2001 (xx slides, in preparation) (4 slides/page)

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