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Transfinite recursion to construct a function on ordinals

score 101 · Answer 1 · 2026-03-25 11:08:41

101

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Transfinite recursion to construct a function on ordinals

Published on 25 Mar 2026 - 11:08

score 180 · Answer 2 · 2015-02-19 11:22:59

180

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Theorem $($Transfinite Induction and Construction$)$ (James Dugundji - 5.1, Page - 40)

Published on 19 Feb 2015 - 11:22

score 10.7k · Answer 3 · 2015-06-29 17:18:41

10.7k

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Principle of Transfinite Induction

Published on 29 Jun 2015 - 17:18

score 3.2k · Answer 4 · 2015-06-29 19:15:20

3.2k

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What are the most prominent uses of transfinite induction outside of set theory?

Published on 29 Jun 2015 - 19:15

score 510 · Answer 5 · 2015-08-24 23:35:01

510

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Lebesgue Premeasure via Transfinite Induction

Published on 24 Aug 2015 - 23:35

score 117 · Answer 6 · 2026-03-23 03:51:04

117

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"Hahn decomposition" for countable or arbitrarily many mutually singular probability measure

Published on 23 Mar 2026 - 3:51

score 2.1k · Answer 7 · 2026-03-22 14:03:00

2.1k

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How does one prove transfinite induction in ZFC?

Published on 22 Mar 2026 - 14:03

score 101 · Answer 8 · 2016-02-09 12:36:48

101

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Using transfinite induction to compute fundamental groups

Published on 09 Feb 2016 - 12:36

score 53 · Answer 9 · 2016-05-27 13:17:08

53

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Could you verify my proof by transfinite induction of: $\langle a_\xi : \xi< \alpha\rangle =\langle b_\xi : \xi< \alpha\rangle$?

Published on 27 May 2016 - 13:17

score 531 · Answer 10 · 2026-02-26 12:36:30

531

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A specific example of transfinite induction

Published on 26 Feb 2026 - 12:36

score 144 · Answer 11 · 2013-05-31 14:17:45

144

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A question on transfinite induction

Published on 31 May 2013 - 14:17

score 53 · Answer 12 · 2017-04-22 11:20:38

53

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How to use induction to prove that if $α+β=β$, then for every $n<ω,α⋅n\le β$ and hence $\alpha\omega\le \beta$?

Published on 22 Apr 2017 - 11:20

score 320 · Answer 13 · 2017-05-04 18:38:44

320

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Prove the limit case: if $\alpha,\beta$ are countable ordinals, then $\alpha+\beta$ is also countable

Published on 04 May 2017 - 18:38

score 507 · Answer 14 · 2017-06-01 14:45:56

507

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Definition of ordinal addition by transfinite induction (ZFC)

Published on 01 Jun 2017 - 14:45

score 156 · Answer 15 · 2017-06-15 18:15:10

156

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Transfinite induction on inductively constructed CW complex

Published on 15 Jun 2017 - 18:15

List Question

Transfinite recursion to construct a function on ordinals

Theorem $($Transfinite Induction and Construction$)$ (James Dugundji - 5.1, Page - 40)

Principle of Transfinite Induction

What are the most prominent uses of transfinite induction outside of set theory?

Lebesgue Premeasure via Transfinite Induction

"Hahn decomposition" for countable or arbitrarily many mutually singular probability measure

How does one prove transfinite induction in ZFC?

Using transfinite induction to compute fundamental groups

Could you verify my proof by transfinite induction of: $\langle a_\xi : \xi< \alpha\rangle =\langle b_\xi : \xi< \alpha\rangle$?

A specific example of transfinite induction

A question on transfinite induction

How to use induction to prove that if $α+β=β$, then for every $n<ω,α⋅n\le β$ and hence $\alpha\omega\le \beta$?

Prove the limit case: if $\alpha,\beta$ are countable ordinals, then $\alpha+\beta$ is also countable

Definition of ordinal addition by transfinite induction (ZFC)

Transfinite induction on inductively constructed CW complex

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