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Duality and definability in first order logic

About this Title

Michael Makkai

Publication: Memoirs of the American Mathematical Society
Publication Year: 1993; Volume 105, Number 503
ISBNs: 978-0-8218-2565-5 (print); 978-1-4704-0080-4 (online)
DOI: https://doi.org/10.1090/memo/0503
MathSciNet review: 1164835
MSC: Primary 03G30; Secondary 03-02, 03C20, 03C40, 18B25

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Table of Contents

Chapters

  • 1. Beth’s theorem for propositional logic
  • 2. Factorizations in 2-categories
  • 3. Definable functors
  • 4. Basic notions for duality
  • 5. The Stone-type adjunction for Boolean pretoposes and ultragroupoids
  • 6. The syntax of special ultramorphisms
  • 7. The semantics of special ultramorphisms
  • 8. The duality theorem
  • 9. Preparing a functor specification
  • 10. Lifting Zawadowski’s argument to ultra*morphisms
  • 11. The operations in $\mathcal {BP}^*$ and $\mathtt {UG}$
  • 12. Conclusion