Jorge Mart\'{\i }nez
Archimedean frames, revisited

Comment.Math.Univ.Carolin. 49,1 (2008) 25-44.

Abstract:This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called {joinfitness} and is {Choice-free}. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. \par There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. \par The concept of an {infinitesimal} element arises naturally, and the join of suitably chosen infinitesimals defines the joinfit nucleus. \par The paper concludes with mostly Choice-free applications of these ideas to commutative rings and their radical ideals.

Keywords: archimedean lattice, joinfit coreflection, infinitesimals, fitness conditions
AMS Subject Classification: 06D22, 18A32, 18A40