Descending chains and antichains of the unary, linear, and monotone subfunction relations

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Abstract

The C -subfunction relations on the set of operations on a finite base set A defined by function classes C are examined. For certain clones C on A , it is determined whether the partial orders induced by the respective C -subfunction relations have infinite descending chains or infinite antichains. More specifically, we investigate the subfunction relations defined by the clone of all functions on A , the clones of essentially at most unary operations, the clones of linear functions on a finite field, and the clones of monotone functions with respect to the various partial orders on A.

Original languageBritish English
Pages (from-to)129-142
Number of pages14
JournalOrder
Volume23
Issue number2-3
DOIs
StatePublished - Aug 2006

Keywords

  • Clones
  • Composition of operations
  • Green's relations
  • Linear functions
  • Menger systems
  • Monotone functions
  • Partial orders
  • Subfunctions

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