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ZFC
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Mon Aug 28 2000 at 20:51:05
The
axiom system
consisting of
ZF
(
Zermelo-Fraenkel set theory
) along with the
axiom of choice
("C"). ZFC is
consistent
if ZF is (as is ZF + the
negation
of C). It is sometimes convenient to state that some
proof
occurs in ZF (i.e. does
not
require the axiom of choice). There are still some who do not accept C, or have some misgivings about it. And even if you accept C, actually using it in a proof immediately makes the result highly non-
constructive
. So a proof in ZF is more constructive.
printable version
chaos
Axiom of Choice
ZF
Zermelo-Fraenkel
inaccessible cardinal
continuum hypothesis
foundations of mathematics
Peano axioms
true arithmetic
Constructive
weakly inaccessible cardinal
cardinal number
sketch of a Set Theory proof that every Goodstein's sequence reaches 0
Finite Plane
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unmeasurable set
Kelley-Morse set theory
Presburger Arithmetic
Axiom of Extensionality
set theory
Smallest number greater than 0
Non-standard analysis
Number
Gödel-Bernays set theory
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