All Questions
9 questions
19
votes
0
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563
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What algebraic properties are preserved by $\mathbb{N}\leadsto\beta\mathbb{N}$?
Given a binary operation $\star$ on $\mathbb{N}$, we can naturally extend $\star$ to a semicontinuous operation $\widehat{\star}$ on the set $\beta\mathbb{N}$ of ultrafilters on $\mathbb{N}$ as ...
- 20.9k
10
votes
0
answers
332
views
Extending models of topological set theory
$\mathsf{GPK_\infty^+}$ is an alternative set theory in which we have comprehension for formulas which are positive in a certain sense; see the SEP article for more detail (or this MO post, which ...
- 20.9k
18
votes
1
answer
1k
views
A topological version of the Lowenheim-Skolem number
This is a continuation of an MSE question which received a partial answer (see below).
Given a topological space $\mathcal{X}$, let $C(\mathcal{X})$ be the ring of real-valued continuous functions on $...
- 20.9k
9
votes
1
answer
410
views
On a result by Rubin on elementary equivalence of homeomorphism groups and homeomorphisms of the underlying spaces
In the known paper On the reconstruction of topological spaces from their group of homeomorphisms by Matatyahu Rubin several deep reconstruction theorems of the form "if $X$ and $Y$ are ...
- 3,011
12
votes
0
answers
241
views
Is there a characterization of the class of first-order formulas that are closed in every compact Hausdorff structure?
Fix a relational language $\mathcal{L}$. (I don't think relational really matters that much but I don't want to worry about it.) A topological $\mathcal{L}$-structure is an $\mathcal{L}$-structure $M$ ...
- 12.5k
10
votes
1
answer
354
views
Elementary equivalence between $n\mapsto n+1$ and its inverse on the Stone-Čech remainder?
Consider structures $(A,f)$ encoding a Boolean algebra $A$ endowed with an automorphism $f$. There is an obvious notion of isomorphism between such structures.
Consider the endomorphism $\hat{\Phi}$ ...
- 63.9k
1
vote
1
answer
1k
views
A new generalisation of dimension? part 2
I worked this theory : A new generalization of the dimension?
I have a theorem about dimensions which is more general and simple than for matroids.
Definition 1: A structure $S$, is a pair $(X, \...
- 4,074
0
votes
0
answers
643
views
A new generalization of the dimension?
During my research, I came a cross on these notions :
Definition 1: A structure $S$, is a pair $(X, \mathcal T)$ with $X$ a set and $\mathcal T$ a set of subsets of $X$, stable by arbitrary ...
- 4,074
11
votes
2
answers
721
views
Inconsistency and workaday independence.
Set-theoretic topologists, for example, encounter many propositions that turn out independent from set theory. Sometimes these results require novel forcing arguments, but often they simply rely on ...
- 17.6k