A theory T extending PA is ω-consistent if there is no formula φ(x) such that T proves φ(n) for every standard numeral n yet also proves ¬∀x φ(x). Strictly stronger than consistency: ω-consistency rules out models containing non-standard…
A theory T extending PA is ω-consistent if there is no formula φ(x) such that T proves φ(n) for every standard numeral n yet also proves ¬∀x φ(x). Strictly stronger than consistency: ω-consistency rules out models containing non-standard…