[FOM] Re: Definition of "large cardinal axiom"?
Timothy Y. Chow
tchow at alum.mit.edu
Wed Apr 14 13:08:18 EDT 2004
Roger Bishop Jones <rbj01 at rbjones.com> wrote:
> Can anyone tell me whether there is a generally accepted
> definition of what is a large cardinal axiom?
Someone once said that the most important concepts in mathematics are
those that don't have a precise definition. "Large cardinal axiom" is one
such concept. Other ones include "sieve method" (in number theory),
"diagonalization argument" (in computational complexity theory), "explicit
formula," "path integral," and maybe even "convergence." In many of these
cases one can get a lot of mileage out of trying to make these concepts
precise, or at least capturing a lot of their essence in a precise
definition, while at the same time leaving the door open to more general
or slightly differing versions of the concept that remain to be discovered
by future generations.
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