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The lattice of interpretability types of varieties

About this Title

O. C. García and W. Taylor

Publication: Memoirs of the American Mathematical Society
Publication Year 1984: Volume 50, Number 305
ISBNs: 978-0-8218-2308-8 (print); 978-1-4704-0718-6 (online)
MathSciNet review: 749524
MSC: Primary 08B05; Secondary 06B99, 20E10

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Table of Contents


  • Introduction
  • The figures
  • Notation used in the figures
  • 1. Preliminaries
  • 2. The categorical point of view
  • 3. The spectrum of $V$ and failures of modularity
  • 4. $\bigwedge $-prime and $\bigwedge $-irreducible elements of $L$
  • 5. Prime and indecomposable filters of $L$; and Mal’tsev conditions
  • 6. Some filters which are not indecomposable or not prime
  • 7. $k^{\textrm {th}}$ root filters
  • 8. Tensor products on $L$
  • 9. Location of varieties in $L$, with emphasis on varieties of groups
  • 10. The bottom part of $L$
  • 11. A proper class between $C$ and $\operatorname {Bin} 1$
  • Open problems
American Mathematical Society