An induction axiom
specifies that a theory includes induction, possibly restricted to specific formulas. IND is the general axiom of induction:
| ϕ(0)∧∀x(ϕ(x)→ϕ(x+1))→∀xϕ(x) for any formula ϕ |
If ϕ is restricted to some family of formulas F then the axiom is called F-IND, or F induction. For example the axiom Σ10-IND is:
| ϕ(0)∧∀x(ϕ(x)→ϕ(x+1))→∀xϕ(x) where ϕ is Σ10 |
| Title |
induction axiom |
| Canonical name |
InductionAxiom |
| Date of creation |
2013-03-22 12:56:51 |
| Last modified on |
2013-03-22 12:56:51 |
| Owner |
Henry (455) |
| Last modified by |
Henry (455) |
| Numerical id |
7 |
| Author |
Henry (455) |
| Entry type |
Definition |
| Classification |
msc 03F35 |
| Synonym |
IND |
| Synonym |
-IND |
| Synonym |
axiom of induction |