Subsystems of Second-order Arithmetic
There are many named subsystems of second-order arithmetic.
A subscript 0 in the name of a subsystem indicates that it includes only a restricted portion of the full second-order induction scheme (Friedman 1976). Such a restriction lowers the proof-theoretic strength of the system significantly. For example, the system ACA0 described below is equiconsistent with Peano arithmetic. The corresponding theory ACA, consisting of ACA0 plus the full second-order induction scheme, is stronger than Peano arithmetic.
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