Finitely many primitive positive clones
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- by S. Burris and R. Willard PDF
- Proc. Amer. Math. Soc. 101 (1987), 427-430 Request permission
Abstract:
Given a finite set $A$ there are only finitely many sequences of the form ${\left \langle {\operatorname {Con}({{\mathbf {A}}^n})} \right \rangle _{n \geq 1}}$ or ${\left \langle {\operatorname {Hom}({{\mathbf {A}}^n},{\mathbf {A}})} \right \rangle _{n \geq 1}}$, where ${\mathbf {A}}$ is any algebra on $A$. From this we derive the fact that there are only finitely many primitive positive clones on $A$, which solves a problem posed by A. F. Danil’čenko in the 1970s. Consequently there are only finitely many model companions for universal Horn classes generated by an algebra of a given finite size.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 427-430
- MSC: Primary 08A40; Secondary 03C50
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908642-5
- MathSciNet review: 908642