|
|
|
|
transfinite induction
|
(Theorem)
|
|
|
Suppose $\Phi(\alpha)$ is a property defined for every ordinal $\alpha$ the principle of transfinite induction states that in the case where for every $\alpha$ if the fact that $\Phi(\beta)$ is true for every $\beta<\alpha$ implies that $\Phi(\alpha)$ is true, then $\Phi(\alpha)$ is true for every ordinal $\alpha$ Formally :
The principle of transfinite induction is very similar to the principle of finite induction, except that it is stated in terms of the whole class of the ordinals.
|
"transfinite induction" is owned by jihemme. [ full author list (2) | owner history (1) ]
|
|
(view preamble | get metadata)
Cross-references: class, terms, principle of finite induction, similar, implies, states, ordinal, property
There are 13 references to this entry.
This is version 7 of transfinite induction, born on 2002-02-25, modified 2002-06-01.
Object id is 2703, canonical name is TransfiniteInduction.
Accessed 9884 times total.
Classification:
| AMS MSC: | 03B10 (Mathematical logic and foundations :: General logic :: Classical first-order logic) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
