Course by V. B. Shehtman "Algebraic logic and categories" (September 14–December 14, 2023, Steklov Mathematical Institute, Room 104 (8 Gubkina))
We kindly ask all participants, including remote ones and those watching recorded videos, to register
at this link.
- Definition and examples of categories. Dual category. Isomorphic objects.
- Definition and examples of functors. Isomorphism and equivalence of
categories. Concretazibility of small categories.
- Limits in categories. Complete categories.
- Adjoint functors. Freyd's theorem.
- The category of $\Omega$-algebras. Term algebras.
- The freedom functor as a left adjoint to the forgetting functor.
- Equational theories and varieties of algebras. Completeness of varieties.
- The freedom functor for a variety. Lindenbaum-Tarski algebras.
- Birkhoff's theorem on varieties.
- Finite, locally finite, and finitely approximable varieties. Harrop's theorem on
decidability.
- Semilattices, lattices, distributive lattices.
- The spectrum of a distributive lattice. Birkhoff-Stone theorem on
representability of distributive lattices.
- Boolean algebras. Stone representation theorem for Boolean algebras. Finite
Boolean algebras.
- Modular and projective lattices.
- Heyting lattices and Heyting algebras.
- Superintuitionistic propositional logics. Soundness and completeness
theorems with respect to Heyting algebras.
- Intuitionistic Kripke frames and their Heyting algebras.
- The canonical Kripke frame of a Heyting algebra. Completeness of
intuitionistic logic wrt Kripke frames.
- Normal modal algebras. Modal algebras of Kripke frames.
- Tarski-Jonsson representation theorem. The canonical Kripke frame of a
modal algebra.
- McKinsey-Tarski theorem on translation of intuitionistic logic into $S4$.
Program
Lecturer
Shehtman Valentin Borisovich
Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center |
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Course by V. B. Shehtman "Algebraic logic and categories", September 14–December 14, 2023 |
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December 14, 2023 (Thu) |
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Lecture 14. Algebraic logic and categories V. B. Shehtman December 14, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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December 7, 2023 (Thu) |
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Lecture 13. Algebraic logic and categories V. B. Shehtman December 7, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 30, 2023 (Thu) |
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Lecture 12. Algebraic logic and categories V. B. Shehtman November 30, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 23, 2023 (Thu) |
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Lecture 11. Algebraic logic and categories V. B. Shehtman November 23, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 16, 2023 (Thu) |
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Lecture 10. Algebraic logic and categories V. B. Shehtman November 16, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 9, 2023 (Thu) |
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Lecture 9. Algebraic logic and categories V. B. Shehtman November 9, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 2, 2023 (Thu) |
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Lecture 8. Algebraic logic and categories V. B. Shehtman November 2, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 26, 2023 (Thu) |
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Lecture 7. Algebraic logic and categories V. B. Shehtman October 26, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 19, 2023 (Thu) |
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Lecture 6. Algebraic logic and categories V. B. Shehtman October 19, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 12, 2023 (Thu) |
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Lecture 5. Algebraic logic and categories V. B. Shehtman October 12, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 5, 2023 (Thu) |
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Лекция 4. Алгебраическая логика и категории V. B. Shehtman October 5, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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September 28, 2023 (Thu) |
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12. |
Лекция 3. Алгебраическая логика и категории V. B. Shehtman September 28, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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September 21, 2023 (Thu) |
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Лекция 2. Алгебраическая логика и категории V. B. Shehtman September 21, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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September 14, 2023 (Thu) |
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14. |
Лекция 1. Алгебраическая логика и категории V. B. Shehtman September 14, 2023 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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