# Tagged Questions

**1**

vote

**1**answer

344 views

### Compactness and completeness in Gödel logic

The standard proof of the completeness theorem in first-order Gödel logic is based
on a first-order countable language. I want to know that is there any proof of the completeness theorem in ...

**9**

votes

**2**answers

281 views

### Extending a partial order while preserving an automorphism

It is well known that if $(P, \leq)$ is a partial order then $\leq$ can always be extended to a linear order. This is sometimes called Szpilrajn´s theorem although it had been previously proved by ...

**3**

votes

**2**answers

414 views

### Cantor theorem on orders

It is "a well-known theorem of Cantor", said Sierpinski (circa 1920), that every countable total order can be imbedded in the rationals, and he proceeds to demonstrate that, assuming the continuum ...

**8**

votes

**2**answers

670 views

### Is $Ded(\kappa)<Ded(\kappa)^\omega$ consistent?

Hello,
I want to ask if anyone can tells us what is known (consistently) about $Ded(\kappa)$, $\kappa$ an infinite cardinal.
Definition If there is a dense linear order w/o endpoints of size ...

**8**

votes

**1**answer

519 views

### Which countable linear orders are $\aleph_0$-categorical?

The question is: Which countable linear orders are $\aleph_0$-categorical?
I have a bit of progress on this:
Define a discrete tuple to be a set of elements, ordered discretely, such that if $a$ and ...

**4**

votes

**2**answers

383 views

### Fraissé limit of the finite linear orderings

Hodges in his Shorter Model Theory promises to show "in what sense the finite linear orderings 'tend to' the rationals rather than, say, the ordering of the integers" (p. 160). After going through his ...

**2**

votes

**3**answers

479 views

### Countable atomless boolean algebra covered by a larger boolean algebra

Suppose Q is an atomless countable boolean algebra, and B is an arbitrary atomless boolean algebra. Q is unique modulo isomorphisms. There is a subalgebra in B that is isomorphic to Q. There is ...