Talk:Pre-intuitionism

Induction
We know that topics like finite field arithmetic do not require induction. We feel (intuitively?) that topics like analysis are consistent with induction. Are there any examples of mathematical/logical systems which are "infinite" in some sense, but for which induction does not work? That is, has anyone created a (more-or-less consistent) system in which induction was intentionally broken, on purpose, but the system still somehow acheives a notion of infinity? Should I be asking this question on the Peano's axioms talk page instead? linas 05:40, 7 September 2005 (UTC)