Dispense e materiale didattico

Elements of Mathematical Logic
Autore: Alessandro Andretta

Versione corrente: link.
Versioni precedenti

Versione del 20 ottobre 2018: link.

Nascondi versioni precedenti

Abstract

Versione preliminare di un libro di logica.

Nascondi abstract

A crèche course in model theory
Autore: Domenico Zambella

Commenti: Lecture notes for an introductory (under)graduate course.
Versione corrente: link.

Abstract

Table of contents

  • Preliminaries and notation
    • Structures
    • Tuples
    • Terms
    • Substructures
    • Formulas
    • Yet more notation
  • Theories and elementarity
    • Logical consequences
    • Elementary equivalence
    • Embeddings and isomorphisms
    • Quotient structures
    • Completeness
    • The Tarski-Vaught test
    • Downward Löwenheim-Skolem
    • Elementary chains
  • Ultraproducts
    • Filters and ultrafilters
    • Direct products
    • Ultraproducts
  • Compactness
    • Compactness via syntax
    • Compactness via ultraproducts
    • Upward Löwenheim-Skolem
    • Finite axiomatizability
  • Types and morphisms
    • Semilattices and filters
    • Distributive lattices and prime filters
    • Types as filters
    • Morphisms
  • Some relational structures
    • Dense linear orders
    • Random graphs
    • Notes and references
  • Fraïssé limits
    • Rich models.
    • Weaker notions of universality and homogeneity
    • The amalgamation property
    • Notes and references
  • Some algebraic structures
    • Abelian groups
    • Torsion-free abelian groups
    • Divisible abelian groups
    • Commutative rings
    • Integral domains
    • Algebraically closed fields
    • Hilbert's Nullstellensatz
  • Saturation and homogeneity
    • Saturated structures
    • Homogeneous structures
    • The monster model
  • Preservation theorems
    • Lyndon-Robinson Lemma
    • Quantifier elimination by back-and-forth
    • Model-completeness
  • Geometry and dimension
    • Algebraic and definable elements
    • Strongly minimal theories
    • Independence and dimension
  • Countable models
    • The omitting types theorem
    • Prime and atomic models
    • Countable categoricity
    • Small theories
    • A toy version of a theorem of Zil'ber
    • Notes and references
  • Definability and automorphisms
    • Many-sorted structures
    • The eq-expansion
    • The definable closure in the eq-expansion
    • The algebraic closure in the eq-expansion
    • Elimination of imaginaries
    • Imaginaries: the true story
    • Uniform elimination of imaginaries
    • Notes and references
  • Invariant sets
    • Invariant sets and types
    • Invariance from the dual perspective
    • Morley sequences and indiscernibles
    • From coheirs to Ramsey to indiscernibles
  • Lascar invariant sets
    • Expansions
    • Lascar strong types
    • The Lascar graph and Newelski's theorem
    • Kim-Pillay types
    • Notes and references
  • Externally definable sets
    • Approximable sets
    • Ladders and definability
    • Vaknik-Chevronenkis dimension
    • Honest definitions
    • Stable theories
    • Stability and the number of types
    • Notes and references

Nascondi abstract

Altro materiale

A boolean algebraic approach to semiproper iterations
Autori: Giorgio Audrito, Silvia Steila, Matteo Viale

Commenti: 60 pagine, in inglese.
Versione corrente: link.

Abstract

The paper gives a self contained development of iterated forcing by means of directed systems of boolean algebras and proves the main results on semiproper iterations expanding and developing on the work of Donder and Fuchs. This material expands on a Ph.D course I gave in summer and fall 2013 on this topic.

Nascondi abstract

Slides

Logica matematica
Autore: Luca Motto Ros

Commenti: 57 slides, in italiano.
Versione corrente: link.

Abstract

Slides per i primi due incontri di un ciclo di quattro seminari introduttivi sulla logica matematica tenuti all\'Università di Milano Bicocca (5-6 maggio 2016).

Nascondi abstract

Calcoli Logici
Autore: Riccardo Camerlo

Commenti: in italiano.
Versione corrente: link.

Abstract

Slides per il terzo incontro di un ciclo di quattro seminari introduttivi sulla logica matematica tenuti all\'Università di Milano Bicocca (12 maggio 2016).

Nascondi abstract

Teoria degli Insiemi
Autore: Riccardo Camerlo

Commenti: in italiano.
Versione corrente: link.

Abstract

Slides per il quarto e ultimo incontro di un ciclo di quattro seminari introduttivi sulla logica matematica tenuti all\'Università di Milano Bicocca (13 maggio 2016).

Nascondi abstract

Video

  • Luca Motto Ros, "Towards the « right » generalization of descriptive set theory to uncountable cardinals" (in inglese).
    15th International Luminy Workshop in Set Theory, Centre International de Rencontres Mathématiques (Marsiglia, Francia), 26 settembre 2019.
    Slides

  • Alessandro Andretta, "È possibile duplicare gli oggetti?" (in italiano).
    Accademia delle Scienze di Torino, 30 gennaio 2019.
    Slides

  • Rapahel Carroy, "A dichotomy for topological embeddability between continuous functions" (in inglese).
    Kurt Gödel Research Center (Vienna, Austria), 22 novembre 2018.

  • Matteo Viale, "The model companions of set theory" (in inglese).
    Set Theory Today: A conference in honor of Georg Cantor, Kurt Gödel Research Center (Vienna, Austria), 27 settembre 2018.
    Slides

  • Luca Motto Ros, "Classical descriptive set theory, generalized descriptive set theory, and I0" (in inglese).
    Set Theory Today: A conference in honor of Georg Cantor, Kurt Gödel Research Center (Vienna, Austria), 21 settembre 2018.
    Slides

  • Alessandro Andretta, "L'ipotesi del continuo" (in italiano).
    Accademia delle Scienze di Torino, 15 febbraio 2018.
    Slides