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PMATH 930

Topics in Logic

Graduate

Winter 2027 · Structural Ramsey Theory

Topics

  • Ramsey classes
  • Hales–Jewett theorem
  • Partite construction
  • Nešetřil–Rödl theorem
  • Ordering property and Fraïssé theory
  • Kechris–Pestov–Todorcevic correspondence
  • Carlson–Simpson theorem
  • Milliken’s tree theorem
  • Big Ramsey degrees
Fall 2024 · Descriptive Set Theory

Topics

  • Polish spaces and Polish groups
  • Baire category methods
  • Standard Borel and Lebesgue spaces
  • Lusin–Novikov theorem
  • Analytic sets and Lusin–Souslin separation
  • Well-founded trees and Souslin operation
  • Borel equivalence relations and Feldman–Moore theorem
Winter 2023 · Model theory of differential fields

Topics

  • in Logic: Model theory of differential fields

Readings

  • There will be no text for the course, the lectures will be essentially self contained. Some external sources may be suggested as we go along.
    unspecified
Fall 2022 · Countably infinite Ramsey theory

Topics

  • Topological dynamics, ultrafilters and forcing in Ramsey theory
  • Infinite Ramsey, Galvin–Prikry and Ellentuck theorems
  • Hindman and van der Waerden theorems
  • Hales–Jewett and Carlson–Simpson theorems
  • Halpern–Läuchli and Milliken theorems
  • Big Ramsey degrees
Winter 2021 · Model theory of difference fields

Topics

  • in Logic: Model theory of difference fields Rahim Moosa Remote learning. Despite early hopes,

Readings

  • There will be no text for the course, the lectures will be essentially self contained. Some external sources may be suggested as we go along.
    unspecified
Fall 2021 · Introduction to Universal Algebra

Topics

  • Lattices and closure operators
  • Algebras, subalgebras, congruences and quotients
  • Homomorphisms and products
  • Subdirect representations
  • Varieties and free algebras
  • Birkhoff’s theorem and Maltsev conditions
  • Equational logic
  • Possible abelian congruences and centrality

Readings

  • A Course in Universal Algebra
    Stanley Burris and H. P. Sankappanavar · Corrected 2012 version · unspecified
    Course generally follows chapters 1–2 of the 1981 Springer book; corrected version linked at http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html
  • Universal Algebra
    Clifford Bergman · unspecified
    CRC Press, 2012; source uses this book’s modern notation.
Fall 2019 · Model Theory

Topics

  • in Logic: Model theory of fields with operators

Readings

  • There will be no text for the course, the lectures will be essentially self contained. Some external sources may be suggested as we go along.
    unspecified
Sources