Intuitionistic Free Abelian Groups
Copyright policy )Intuitionistic Free Abelian Groups
The paper provides an intuitionistic construction of free abelian groups over arbitrary sets. It shows that a subgroup of a free abelian group is not necessarily itself free abelian, and that \(''free=projective''\Rightarrow full\) AC, for abelian groups. The paper uses Kripke models. The second part deals with the conditions for admitting an apartness relation on free abelian groups. An axiomatization of the {\#}-free part of free abelian groups with apartness is given and it is shown that this is essentially infinite.
- Utrecht University Netherlands
apartness, Wijsbegeerte, intuitionistic construction, axiomatization, Applications of logic to group theory, Torsion-free groups, infinite rank, Intuitionistic mathematics, Kripke model, free abelian groups
apartness, Wijsbegeerte, intuitionistic construction, axiomatization, Applications of logic to group theory, Torsion-free groups, infinite rank, Intuitionistic mathematics, Kripke model, free abelian groups
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