induction axiom

An induction axiomMathworldPlanetmath specifies that a theory includes inductionMathworldPlanetmath, possibly restricted to specific formulasMathworldPlanetmathPlanetmath. 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