Question

Let $P, Q, R$ be finite posets. Prove that $P^{Q+R} \cong P^Q \times P^R$.

score 76 · Answer 1 · 2014-08-29 19:56:33

76

Views

Let $P, Q, R$ be finite posets. Prove that $P^{Q+R} \cong P^Q \times P^R$.

Published on 29 Aug 2014 - 19:56

score 722 · Answer 2 · 2014-08-29 21:31:08

722

Views

Let $P$ be a finite poset. Show that the number of order ideals equals the number of antichains.

Published on 29 Aug 2014 - 21:31

score 119 · Answer 3 · 2014-08-29 22:27:33

119

Views

Prove that $P$ is a lattice (details inside)

Published on 29 Aug 2014 - 22:27

score 4.2k · Answer 4 · 2014-08-29 22:59:38

4.2k

Views

Let $L$ and $L'$ be lattices. Prove that $L \times L'$ is also a lattice.

Published on 29 Aug 2014 - 22:59

score 516 · Answer 5 · 2026-03-27 09:57:03

516

Views

Are $1+ω$ and $ω+1$ isomorphic?

Published on 27 Mar 2026 - 9:57

score 1.1k · Answer 6 · 2026-03-28 10:16:39

1.1k

Views

Every subgroup of a cyclic group is characteristic (using lattice theory).

Published on 28 Mar 2026 - 10:16

score 81 · Answer 7 · 2014-08-31 02:57:59

81

Views

Correctness of proof that every positive rational with square $>2$ is an upper bound for those with square $<2$

Published on 31 Aug 2014 - 2:57

score 111 · Answer 8 · 2014-08-31 23:10:52

111

Views

Dilworths Theorem proof doubt

Published on 31 Aug 2014 - 23:10

score 597 · Answer 9 · 2014-09-02 00:26:27

A question about the cardinality of a set of functions with finite support where the domain of each function has cardinality aleph-null.

score 93 · Answer 10 · 2014-09-02 04:17:57

93

Views

Well-ordered family of open sets.

Published on 02 Sep 2014 - 4:17

score 89 · Answer 11 · 2026-03-29 09:08:41

89

Views

Is it Preference relation?

Published on 29 Mar 2026 - 9:08

score 417 · Answer 12 · 2026-03-29 07:29:25

417

Views

An accessible example of a preorder that is neither symmetric nor antisymmetric

Published on 29 Mar 2026 - 7:29

score 2.3k · Answer 13 · 2026-03-29 07:28:40

2.3k

Views

Prove that the binary relation "is a subset of" is a...

Published on 29 Mar 2026 - 7:28

score 126 · Answer 14 · 2014-09-04 16:26:21

126

Views

Constructing order embeddings between Boolean algebras from embeddings from their finite subalgebras

Published on 04 Sep 2014 - 16:26

score 80 · Answer 15 · 2014-09-06 16:11:55

80

Views

If a poset is Dedekind-complete, is its opposite necessarily Dedekind-complete?

Published on 06 Sep 2014 - 16:11

List Question

Let $P, Q, R$ be finite posets. Prove that $P^{Q+R} \cong P^Q \times P^R$.

Let $P$ be a finite poset. Show that the number of order ideals equals the number of antichains.

Prove that $P$ is a lattice (details inside)

Let $L$ and $L'$ be lattices. Prove that $L \times L'$ is also a lattice.

Are $1+ω$ and $ω+1$ isomorphic?

Every subgroup of a cyclic group is characteristic (using lattice theory).

Correctness of proof that every positive rational with square $>2$ is an upper bound for those with square $<2$

Dilworths Theorem proof doubt

A question about the cardinality of a set of functions with finite support where the domain of each function has cardinality aleph-null.

Well-ordered family of open sets.

Is it Preference relation?

An accessible example of a preorder that is neither symmetric nor antisymmetric

Prove that the binary relation "is a subset of" is a...

Constructing order embeddings between Boolean algebras from embeddings from their finite subalgebras

If a poset is Dedekind-complete, is its opposite necessarily Dedekind-complete?

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