Reverse Mathematics of the Nielsen-Schreier Theorem
نویسندگان
چکیده
The Nielsen-Schreier Theorem states that every subgroup of a free group is free. To formalize this theorem in weak subsystems of second order arithmetic, one has to choose between defining a subgroup in terms of a set of group elements and defining it in terms of a set of generators. We show that if subgroups are defined by sets, then the Nielsen-Schreier Theorem is provable in RCA0, while if subgroups are defined by generators, the theorem is equivalent to ACA0.
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