First-order continuous induction and a logical study of real closed fields (Q2287034)

The present paper concerns the principle of ``continuous induction'' and various forms of it. The authors study three forms of the principle of continuous induction, and show that two of them are equivalent to each other and to the completeness principle over the theory of ordered fields, while the third form is weaker. They also show that the weak principle of continuous induction is equivalent to the Archimedean property of ordered abelian groups.