6
votes
2answers
337 views

How big $|Aut(M)|$ can be, given $|\partial Aut(M)|$?

My apologies: There were a couple of typos in the original question. Hope I got them all. Let $\kappa$ be an uncountable cardinal of cofinality $\omega$ and $M$ a model of size $\kappa$. We equip ...
3
votes
0answers
205 views

When Aut(M) preserves a linear order?

I have a general-type question: Suppose $M$ is a countable structure that is ultrahomogeneous, i.e. every (partial) isomorphism between finitely generated substructures of $M$ extends to an ...
13
votes
0answers
567 views

Does ZF prove that topological groups are completely regular?

Let $\mathbf{G} = \langle G,\cdot,\mathcal{T}\;\rangle$ be a topological group. Let $\mathbf{e}$ be the identity element of $\langle G,\cdot \rangle$. Assume $\{\mathbf{e}\}$ is closed in $\langle ...
5
votes
1answer
223 views

A restatement, in terms of the semi-group product of the left-invariant completion of a Polish group, of http://mathoverflow.net/questions/71389

This is a re-statement, of sorts, of Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation property?, so far unanswered. Let $G$ be a ...