Attività settimanale

  • Introduzione

    Minimizza tutto Espandi tutto

  • Week I

    Tuesday 23 September 12:30-14:30 Lecture 1
    Saturated models and definability (review). Lyndon-Robinson Lemma. Blackboard
    Wednesday 24 September 12:30-14:30 Lecture 2
    Back-and-forth and quantifier elimination. Blackboard

  • Week II

    Tuesday 30 September 12:30-14:30 Lecture 3
    The omitting types theorem. Counterexample to the omitting types theorem for uncountable languages. Blackboard
    Wednesday 1 October 12:30-14:30 Lecture 4
    Prime and atomic models. Characterization of ω-categoricity. Strongly minimal and ω-categorical theories (to be continued). Blackboard

  • Week III

    Tuesday 7 October 12:30-14:30 Lecture 5
    (Continuing) Strongly minimal, ω-categorial theories have the finite model property (in particular they are not finitely axiomatizable). Binary trees of formulas. Small theories. Countable saturated models and existence of atomic models. Blackboard
    Wednesday 8 October 12:30-14:30 Lecture 6
    Exercise: no complete theory ha exactly two countable models. Many-sorted models. The eq-expansion. Blackboard

  • Week IV

    Tuesday 14 Oktober 12:30-14:30 Lecture 7
    Definable and algebraic elements in the eq-expansion. The finite equivalence relation theorem. Shelah strong types. Blackboard
    Wednesday 15 October 12:30-14:30 Lecture 8
    Elimination of imaginaries and weak elimination. Various characterizations. Elimination of imaginaries in ACFs and random graphs. Blackboard

  • Week V

    Tuesday 21 Oktober 12:30-14:30 Lecture 9
    Invariant set and types. Types that are finitely satisfiable in a given set. Extensions of finitely satisfiable types. Blackboard
    Wednesday 22 October 12:30-14:30 Lecture 10
    Morley sequences. Indiscernible sequences. Properties of the coheir-heir relation. Blackboard

  • Week VI

    Tuesday 28 Oktober 12:30-14:30 Lecture 11
    Characterization of coheir sequences using the heir-coheir relation. The Ramsey theorem. Blackboard
    Wednesday 29 October 12:30-14:30 Lecture 12
    Ehrenfeucht-Mostowski theorem. The * operation on semigroups. Blackboard

  • Week VII

    Tuesday 4 November 12:30-14:30 Lecture 13
    Existence of idempotents. Hindman's theorem. Blackboard
    Wednesday 5 November 12:30-14:30 Lecture 14
    Minimal left ideals. The Ellis group. Blackboard

  • Week VIII

    Tuesday 11 November 12:30-14:30 Lecture 15
    The Hales-Jewett theorem (proof). Blackboard
    Wednesday 12 November 12:30-14:30 Lecture 16
    Stable relations and formulas. Approximable (externally definable) sets. Blackboard

  • Week IX

    Tuesday 18 November 12:30-14:30 Lecture 17
    Sets externally definable by stable formulas are definable. Stable formulas yield a small number of types. Blackboard

  • Week X

    Tuesday 25 November 12:30-14:30 Lecture 18
    Lascar invariance and Lascar types. The Lascar graph. Coheirs over sets. Blackboard
    Wednesday 26 November 12:30-14:30 Lecture 19
    For stable formulas almost satisfiablility is partition regular. Stability and the symmetry of forking. Blackboard

  • Week XI

    Tuesday 2 December 12:30-14:30 Lecture 20
    Properties equivalent to nonforking for stable formulas. Stationarity. Blackboard
    Wednesday 3 December 12:30-14:30 Lecture 21
    Syndetic, thick, invariant, and wide formulas and types. Blackboard

  • Week XII

    Tuesday 9 December 12:30-14:30 Lecture 22
    Strongly syndetic and weakly thick sets. The thick=wide phenomenon. Stationarity. Blackboard

  • Week XIII

    Tuesday 16 December 12:30-14:30 Lecture 23
    The thick=wide equality for stable formulas. Blackboard

  • Esame

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      Data limite: venerdì, 23 gennaio 2026, 13:00
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