Arithmetical comprehension theory
= Arithmetical comprehension theory
{title2=$\mathrm{ACA}_0$}
This subsystem of second-order arithmetic allows comprehension for arithmetical formulas and induction in its standard restricted presentation. Its first-order arithmetical consequences are those of <Peano arithmetic>. It is a useful base for comparing <well-quasi-ordering> principles with <ordinal> notation systems without assuming their global well-foundedness.