# Tagged Questions

32 views

### Is an o-minimal structure equivalent to a totally ordered set?

Is the notion of o-minimality synonymous to a totally ordered set? Both notions seem to emanate from Tarski although he may not have discussed o-minimality explicitly...
63 views

### isomorphism between divisible, totally ordered, abelian groups

Let $G$, $H$ be divisible, abelian, linearly ordered groups, whose cardinalities are equal and satisfy $\mu := |G|=|H|>\aleph_{0}$. These are supposed to be (order!) isomorphic. And just about ...
81 views

### Infinite linear order with endpoints which is non-dense

In the process of answering questions about normal models, I had to prove the following: Any normal model of $\chi$ is a non-dense linear order with a least and greatest element. The next question ...
75 views

### Does model theory extend to partial functions?

I have been reading a bit about effect algebras and d-posets recently, sets $M$ on which you have a single partial binary operation (partial here meaning partially defined, i.e. the domain of this ...
202 views

### Is this a characterization of well-orders?

While grading some papers and thinking about a question related to well-orders (in particular, pointing a mistake in a solution), I came to think of a reasonable characterization for well-orders. I ...
121 views

### Show that Total Orders does not have the finite model property

I am not sure whether my answer to this problem is correct. I would be grateful if anyone could correct my mistakes or help me to find the correct solutions. The problem: Show that Total Orders ...
73 views

### $T\vDash\psi$ equivalences

$T\vDash\psi$ means $T$ satifies $\psi$ from Tarski's definition of truth, it simply means that the sentence $\psi$ is valid in $M$. I call a sentence $\psi$ universally if it is valid in every ...
123 views

### Semi-formal language - Universe has at least three elements

First of all I would like to construct a semi formal sentence, such that the universum has at least three elements. My attempt: $$\exists x\exists y\exists z (x\not=y\wedge y\not=z\wedge x\not=z)$$ ...
211 views

247 views

### Why is a commutative ring with an infinite number of idempotent elements unstable?

In a book of model theory I found the following statement: A commutative ring with an infinite number of idempotent elements unstable. I haven't manage to prove it yet. As stability in the model ...
It is well known that for every infinite cardinal $\kappa$ the number of non-isomorphic total orders of cardinality $\kappa$ is $2^\kappa$. Who first proved this, and in what context? Was it proved ...
### Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
I'm trying to knock out a few of the later exercises from Enderton's Elements of Set Theory. This problem is #17, found on page 227. A partial ordering $R$ is said to be dense iff whenever $xRz$, ...