[FOM] Ordinals as hereditarily transitive sets

[Aldo Antonelli]

Sorry to be coming late to this thread.

Concerning the various definitions of the ordinals, I believe they are
not all equivalent in the absence of the Axiom of Foundation
(Regularity), and this is something people in AFA and related theories
might care about (one might still want the ordinals around for
transfinite recursion, for instance, even in the presence of the
Anti-Foundation Axiom).

I seem to recall asking Larry Moss about this (longer ago than Larry
or I probably care to remember), and he pointed out that Robinson's
1937 definition (an ordinal is a transitive set linearly ordered by
epsilon) works in non-well-founded contexts as well.

Larry can correct me if this is not quite accurate.

-- Aldo

*****************************************
G. Aldo Antonelli
Professor of Philosophy
University of California, Davis
http://aldo-antonelli.org
antonelli at ucdavis.edu +1 530 554 1368