In the ZF set theory ordinals are transitive sets which are well-ordered by $\in$. They are canonical representatives for well-orderings under order-isomorphism. In addition to the intriguing ordinal arithmetics, ordinals give a sturdy backbone to models of ZF and operate as a direct extension of the positive integers for *transfinite* inductions.
Stats
created |
1 year ago |
viewed |
8 times |
editors |
0 |
Recent Hot Answers
What are some good open problems about countable ordinals?Ordinals Addition Property
When does ordinal addition/multiplication commute?
Do we get predicative ordinals above $\Gamma_0$ if we use hyperexponentiation?
How many positive numbers need to be added together to ensure that the sum is infinite?
more »
Related Tags
set-theory × 131elementary-set-theory × 66
cardinals × 35
general-topology × 28
order-theory × 20
homework × 20
logic × 16
axiom-of-choice × 10
transfinite-recursion × 6
definition × 6
reference-request × 6
computability × 5
notation × 5
descriptive-set-theory × 5
induction × 3
compactness × 3
metric-spaces × 3
terminology × 3
abstract-algebra × 3
infinity × 3
commutative-algebra × 2
category-theory × 2
functions × 2
constructive-mathematics × 2
sequences-and-series × 2
