Question

Fields that can be ordered in more than one way

score 1.6k · Answer 1 · 2016-12-23 04:47:29

1.6k

Views

Fields that can be ordered in more than one way

Published on 23 Dec 2016 - 4:47

score 592 · Answer 2 · 2016-12-29 00:29:08

592

Views

How to prove that every ordered field has a subfield isomorphic to $\mathbb{Q}$ using a certain provided function?

Published on 29 Dec 2016 - 0:29

score 27 · Answer 3 · 2017-01-02 22:23:34

27

Views

For all $f$ in a totally ordered field, $0\,{\preceq}\,f*f$

Published on 02 Jan 2017 - 22:23

score 261 · Answer 4 · 2017-01-05 19:53:54

261

Views

Proving transitivity of ${\le}$ on $\mathbb{Q}$

Published on 05 Jan 2017 - 19:53

score 40 · Answer 5 · 2017-01-05 21:59:01

40

Views

$(f_1\,{\preceq}\,f_2)\,{\land}\,0_F\,{\preceq}\,f_3{\implies}f_1f_3\,{\preceq}\,f_2f_3$

Published on 05 Jan 2017 - 21:59

score 133 · Answer 6 · 2017-01-06 17:11:14

133

Views

What's wrong with this proof that ordering on rationals isn't well-defined?

Published on 06 Jan 2017 - 17:11

score 314 · Answer 7 · 2017-01-10 21:07:43

314

Views

How to prove that a non-Archimedean ordered field implies that it doesn't have least upper bound property?

Published on 10 Jan 2017 - 21:07

score 810 · Answer 8 · 2017-01-17 18:10:08

810

Views

Least upper bound property implies that the orderered field in question is Archimedean

Published on 17 Jan 2017 - 18:10

score 47 · Answer 9 · 2017-01-21 00:53:28

47

Views

The set of all open intervals is a basis on any totally ordered field

Published on 21 Jan 2017 - 0:53

score 49 · Answer 10 · 2017-01-26 16:03:13

49

Views

For all elements $x$ in any Archimedean ordered field, there is a $q \in \mathbb Q:q<x$

Published on 26 Jan 2017 - 16:03

score 47 · Answer 11 · 2017-01-27 12:41:24

47

Views

For any element of Archimedean ordered field there is a greater natural number

Published on 27 Jan 2017 - 12:41

score 351 · Answer 12 · 2017-02-04 09:10:23

351

Views

Can the linear polynomials be totally ordered?

Published on 04 Feb 2017 - 9:10

score 679 · Answer 13 · 2017-03-12 16:29:59

679

Views

Can a field with cardinality $3$ be an ordered field?

Published on 12 Mar 2017 - 16:29

score 184 · Answer 14 · 2017-03-12 17:31:12

184

Views

Do all fields with internal absolute values arise either as ordered fields or like $\mathbb{C}$ from them?

Published on 12 Mar 2017 - 17:31

score 43 · Answer 15 · 2017-03-15 19:55:31

43

Views

Real closure and archimedean-like property

Published on 15 Mar 2017 - 19:55

List Question

Fields that can be ordered in more than one way

How to prove that every ordered field has a subfield isomorphic to $\mathbb{Q}$ using a certain provided function?

For all $f$ in a totally ordered field, $0\,{\preceq}\,f*f$

Proving transitivity of ${\le}$ on $\mathbb{Q}$

$(f_1\,{\preceq}\,f_2)\,{\land}\,0_F\,{\preceq}\,f_3{\implies}f_1f_3\,{\preceq}\,f_2f_3$

What's wrong with this proof that ordering on rationals isn't well-defined?

How to prove that a non-Archimedean ordered field implies that it doesn't have least upper bound property?

Least upper bound property implies that the orderered field in question is Archimedean

The set of all open intervals is a basis on any totally ordered field

For all elements $x$ in any Archimedean ordered field, there is a $q \in \mathbb Q:q<x$

For any element of Archimedean ordered field there is a greater natural number

Can the linear polynomials be totally ordered?

Can a field with cardinality $3$ be an ordered field?

Do all fields with internal absolute values arise either as ordered fields or like $\mathbb{C}$ from them?

Real closure and archimedean-like property

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