The subscript 0 in ACA0 indicates that not every instance of the induction axiom scheme is included this subsystem. This makes no difference for ω-models, which automatically satisfy every instance of the induction axiom. It is of importance, however, in the study of non-ω-models. The system consisting of ACA0 plus induction for all formulas is sometimes called ACA with no subscript. The system ACA0 is a conservative extension of first-order arithmetic (or first-order Peano axioms), defined as the basic axioms, plus the first-order induction axiom scheme (for all formulas φ involving no class variables at all, bound or otherwise), in the language of first-order arithmetic (which does not permit class variables at all). In particular it has the same proof-theoretic ordinal ε0 as first-order arithmetic, owing to the limited induction schema. A formula is called "bounded arithmetical", or Δ00, when all its quantifiers are of the form ∀"n"01 (or sometimes Σ1), respectively Π01 (or sometimes Π1) when it of the form ∃"m"•(φ), respectively ∀"m"•(φ) where φ is a bounded arithmetical formula and "m" is an individual variable (that is free in φ). More generally, a formula is called Σ0"n", respectively Π0"n" when it is obtained by adding existential, respectively universal, individual quantifiers to a Π0"n"−1, respectively Σ0"n"−1 formula (and Σ00 and Π00 are all equivalent to Δ00). By construction, all these formulas are arithmetical (no class variables are ever bound) and, in fact, by putting the formula in Skolem prenex form one can see that every arithmetical formula is equivalent to a Σ0"n" or Π0"n" formula for all large enough "n". The subsystem RCA0 is a weaker system than ACA0 and is often used as the base system in reverse mathematics. It consists of: the basic axioms, the Σ01 induction scheme, and the Δ01 comprehension scheme. The former term is clear: the Σ01 induction scheme is the induction axiom for every Σ01 formula φ. The term “Δ01 comprehension” is more complex, because there is no such thing as a Δ01 formula.