All Questions
Tagged with set-theory posets
9 questions with no upvoted or accepted answers
9
votes
0
answers
250
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Distributivity of certain infinite products
Suppose we have a sequence of posets $\{\mathbb P_n : n\in\omega\}$ such that for each $n$, $\mathbb P_{n+1}$ is $|\mathbb P_n|^+$-distributive. Is $\prod_{n>0} \mathbb P_n$ necessarily $|\mathbb ...
- 18.6k
6
votes
0
answers
170
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Katetov ordering on ideals on $\omega$
Recall that a nonempty set ${\cal I}\subseteq {\cal P}(\omega)$ is a (set) ideal if
$B\in{\cal I}$ and $A\subseteq B$ imply $A\in{\cal I}$, and
$A,B \in {\cal I}$ implies $A\cup B\in {\cal I}$.
By $\...
- 48.9k
4
votes
0
answers
300
views
Is the set of approximating sequences for irrationals dominating?
Let $r\in [0,1]\setminus\mathbb{Q}$, let $\mathbb{N}$ denote the set of non-negative integers and let $\mathbb{N}_+=\mathbb{N}\setminus\{0\}$. For $n\in\mathbb{N}_+$ let $$\alpha_r(n)=\min\{|r-\frac{...
- 48.9k
4
votes
0
answers
160
views
Finite pre-orders embeddable in the Rudin-Keisler ordering
$\DeclareMathOperator{\NPU}{\operatorname{NPU}}\DeclareMathOperator{\RK}{\,\mathrm{RK}}$A pre-ordered set is a pair $(P, \leq)$ where $P$ is a set and $\leq\subseteq P\times P$ is a reflexive and ...
- 48.9k
4
votes
0
answers
435
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Can infinite bounded distibutive lattices be "arbitrarily wide"?
I was always thinking, in an informal way, that the powerset lattices ${\cal P}(X)$ (where $X$ is an infinite set) are the "widest" bounded distributive lattices with respect to their height. (In ${\...
- 48.9k
4
votes
0
answers
153
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Maximality with respect to having no marriage
Let $A,B\neq \emptyset$ be disjoint and suppose $G = (A\cup B, E)$ is bipartite where for all $e\in E$ we have $e\cap A \neq \emptyset\neq e\cap B$. For $a\in A$ we set $N_G(a) = \{b\in B: (\exists e\...
- 48.9k
2
votes
0
answers
92
views
Can this order relation, defined in terms of all topological spaces, be defined in terms of the reals alone?
Let $K$ be the operator monoid under composition of Kuratowski's $14$ set operators generated by topological closure $k$ and complement $c.$ Kuratowski's 1922 paper gives the poset diagram of the ...
- 870
2
votes
0
answers
131
views
non-degenarete tools to calculate a derived functor on a model category which is a poset?
Are there theorems (esp. computational tools) on model categories which survive and do not trivialise when its underlying category is a (quasi-)poset ? Are there tools
that may help to calculate a ...
- 1,299
1
vote
0
answers
78
views
Set-theoretic trees with ordering between siblings
In set-theoretic trees, we have the binary relation $<_T$ (which defines the "ancestor-descendant" ordering). This relation is partial, as children are incomparable in that ordering.
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