7,814 reputation
12049
bio website tuwien.ac.at/goldstern
location
age
visits member for 4 years, 3 months
seen Aug 27 at 9:41

Aug
13
comment Reconstructing relations with the image relation of a topology
@EricWofsey @ Joel Right.
Aug
12
comment Reconstructing relations with the image relation of a topology
If $R$ is an equivalenc relation on an arbitrary set, can't you just put a well-order on the classes, and repeat your argument? "$f$ must take the least class to itself, and so on, now transfinitely"?
Aug
12
comment Reconstructing relations with the image relation of a topology
I assume you want your pre-order to be linear (or "total").
Aug
12
comment Hausdorff spaces with asymmetric image relation
Of course! Thank you.
Aug
12
answered Hausdorff spaces with asymmetric image relation
Aug
11
comment “Universal” connected spaces
$\kappa+1$ usually means $\kappa\cup \{\kappa\}$, or in order theoretic terms: the order of $\kappa$ (viewed as an ordinal), extended by an additional top element.
Aug
5
comment A question on the name of a property
@FrodeBjørdal Rather than quoting my own book I can point to Shoenfield's book (4.2, page 45), which uses this notation. (But requires constants, not just any terms.) Also Hinman (Fundamentals of Math.Logic 3.1, page 196) calls a complete theory "Henkin complete" if there are "Henkin witnesses" for every closed existential formula. This concept is used for Henkin's proof of Gödel's completeness theorem.
Aug
4
comment A question on the name of a property
If you require this property only for closed formulas of the form $\exists x\, F(x)$, then I would call $T$ a Henkin theory.
Jul
30
answered A group topology which commutes with closed subgroups
Jul
29
comment Does a continuous map $f$ from the $n$-ball $B$ into $R^n$ such that $B\subset f(B)$ have a fixed point?
The new answer is even nicer than mine.
Jul
28
revised Online introduction to Lattice Theory?
not to be confused: number theory, universal algebra
Jul
23
comment Löwenheim-Skolem for many-sorted theories
Consider the two-sorted theory of "sets" and "elements". If your theory contains the extensionality axiom, then any model with $\kappa$ many "elements" has at most $2^\kappa$ many "sets". -- This can be iterated finitely many times.
Jul
22
comment Contracting join-incomplete lattice endomorphisms
You use $f$ both for the given homomorphism and for the one you are looking for. Please call one of them $g$.
Jul
15
comment Why is the set-theoretic principle $\diamondsuit$ called $\diamondsuit$?
@JoelDavidHamkins Just a stupid joke. The two halves of the diamond look like two-dimensional corner reflectors (en.wikipedia.org/wiki/Corner_reflector), so one reflects downwards, the other upwards.
Jul
14
accepted Why is the set-theoretic principle $\diamondsuit$ called $\diamondsuit$?
Jul
14
comment Why is the set-theoretic principle $\diamondsuit$ called $\diamondsuit$?
@JoelDavidHamkins So $\curlyvee$ and $\curlywedge$ stand for upward and downward reflection?
Jul
13
answered Does a continuous map $f$ from the $n$-ball $B$ into $R^n$ such that $B\subset f(B)$ have a fixed point?
Jul
13
asked Why is the set-theoretic principle $\diamondsuit$ called $\diamondsuit$?
Jul
8
answered Incomplete lattice homomorphisms between complete lattices
Jun
27
revised Preserving $\omega_1$ is Inaccessible to the reals
typos corrected: Schindler