Question

How to show that $(\Bbb Q, <)$ contains an order isomorphic copy of $\epsilon_0$ which is the least ordinal satisfies $\omega^\epsilon = \epsilon$?

score 357 · Answer 1 · 2026-04-02 20:38:04

How to show that $(\Bbb Q, <)$ contains an order isomorphic copy of $\epsilon_0$ which is the least ordinal satisfies $\omega^\epsilon = \epsilon$?

score 197 · Answer 2 · 2013-05-24 18:26:04

197

Views

What's so well in having a least element in a set?

Published on 24 May 2013 - 18:26

score 713 · Answer 3 · 2013-05-25 04:36:49

713

Views

Ask book to deeply understand partially ordered sets

Published on 25 May 2013 - 4:36

score 135 · Answer 4 · 2013-05-26 10:37:54

135

Views

How to build linear order on $\mathcal P({\bf N})$

Published on 26 May 2013 - 10:37

score 953 · Answer 5 · 2013-05-27 07:51:07

953

Views

Every preorder is a topological space

Published on 27 May 2013 - 7:51

score 202 · Answer 6 · 2026-04-01 03:47:13

202

Views

Is an orthocomplemented lattice automatically complete?

Published on 01 Apr 2026 - 3:47

score 114 · Answer 7 · 2013-05-28 18:19:36

114

Views

Composition of linear orders on the same set

Published on 28 May 2013 - 18:19

score 136 · Answer 8 · 2013-05-28 21:17:37

136

Views

Are there any texts on order theory that treat it as decategorified category theory?

Published on 28 May 2013 - 21:17

score 685 · Answer 9 · 2026-03-30 06:45:30

685

Views

Presheaves over sieves and posets

Published on 30 Mar 2026 - 6:45

score 40 · Answer 10 · 2013-05-29 04:47:08

40

Views

Infinite linear ordered set which doesn't include infinte well-ordered subsets

Published on 29 May 2013 - 4:47

score 559 · Answer 11 · 2026-04-02 20:32:00

559

Views

Do there exist totally ordered sets with the 'distinct order type' property that are not well-ordered?

Published on 02 Apr 2026 - 20:32

score 58 · Answer 12 · 2013-05-30 15:57:08

58

Views

On the general definition and nature of preordered sets

Published on 30 May 2013 - 15:57

score 157 · Answer 13 · 2026-04-01 05:23:06

In any poset, the existence of arbitrary joins is equivalent to the existence of arbitrary meets. But, is there a general principle?

score 206 · Answer 14 · 2013-05-31 13:33:52

206

Views

Problem with a definition of $\succsim$-maximal element and $\succsim$-maximum

Published on 31 May 2013 - 13:33

score 211 · Answer 15 · 2026-04-01 05:17:06

211

Views

Why are complete lattice homomorphisms defined that way?

Published on 01 Apr 2026 - 5:17

List Question

How to show that $(\Bbb Q, <)$ contains an order isomorphic copy of $\epsilon_0$ which is the least ordinal satisfies $\omega^\epsilon = \epsilon$?

What's so well in having a least element in a set?

Ask book to deeply understand partially ordered sets

How to build linear order on $\mathcal P({\bf N})$

Every preorder is a topological space

Is an orthocomplemented lattice automatically complete?

Composition of linear orders on the same set

Are there any texts on order theory that treat it as decategorified category theory?

Presheaves over sieves and posets

Infinite linear ordered set which doesn't include infinte well-ordered subsets

Do there exist totally ordered sets with the 'distinct order type' property that are not well-ordered?

On the general definition and nature of preordered sets

In any poset, the existence of arbitrary joins is equivalent to the existence of arbitrary meets. But, is there a general principle?

Problem with a definition of $\succsim$-maximal element and $\succsim$-maximum

Why are complete lattice homomorphisms defined that way?

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