# Tagged Questions

**4**

votes

**1**answer

144 views

### Universal graphs on higher cardinals

The Rado graph contains every finite graph as induced subgraph, and its also holds for countable graphs. So it is an universal graph of size $\aleph_0$, which contains all graphs of size $\aleph_0$ as ...

**7**

votes

**0**answers

181 views

### Is there a Rado category?

The Rado graph appears to have a nice universality property (it contains all finite and all countably infinite graphs as induced subgraphs) and homogeinety property (any isomorphism between ...

**1**

vote

**1**answer

246 views

### Self-containing graphs

[Second try, after this question failed.]
Let me sketch a notion of self-containing structures by a simple example. Consider the class $\Gamma$ of finite or countable digraphs ("graphs" for short) ...

**1**

vote

**0**answers

147 views

### Self-modelling structures

Consider - for the sake of simplicity - only graphs as structures.
For undirected graphs $(V, E\subseteq \binom{V}{2})$ let
$E(v)$ be the set of edges $e\in E$ incident with $v$, i.e. $\lbrace e ...

**2**

votes

**1**answer

192 views

### Definability in a language with a single binary predicate

Let the first-order language ${\mathcal{L}}$ have a single binary predicate $P$. Consider the structure whose underlying set is ${\mathbb{Z}}$, the integers, and an ordered pair $(m,n)$ is in $P$ if ...

**3**

votes

**1**answer

394 views

### Examples of Graphs with Trivial Definable Closure

If I'm giving a lecture on trivial definable closure (as a property of graphs), what is a good example of a graph that I can easily draw to depict the concept of trivial dcl?

**2**

votes

**1**answer

391 views

### Ergodic Invariant Measures and the Rado graph

Given two or more invariant measures on a structure, there are various ways to combine them to form another invariant measure on the structure. For example, given two invariant measures on a ...

**6**

votes

**4**answers

649 views

### Self-defining structures

The relations $R$ in abstract graphs (with genuinely propertyless vertices) cannot be defined because there is nothing the relations can base on: they have to be presupposed.
But consider derived ...

**2**

votes

**0**answers

156 views

### Semantics of neural network-like structures

Background
Language (of mathematicians and most other people) has a sequential surface structure and a tree-like deep structure. So semantics usually is the semantics of such syntactical structures: ...

**7**

votes

**3**answers

467 views

### Statistics for Second order properties of Random graphs

Hi!
Let G(N) be the number of graphs with vertices {1, 2, ..., N} and GN(F) be the number of those of them which satisfy graph property F. There is a beautiful result by Glebskii and Fagin that limit ...

**14**

votes

**1**answer

556 views

### Which graphs are elementarily equivalent to their own disjoint sums?

In Stefan Geschke's recent
question,
one of the solutions observed that the graph consisting of
a single infinite beaded chain, a $\mathbb{Z}$-chain where
each integer is connected to its nearest ...

**10**

votes

**3**answers

1k views

### Is non-connectedness of graphs first order axiomatizable?

A recent
question
asked for graph properties that are first order axiomatizable but not finitely axiomatizable.
Connectedness was mentioned in the context. Connectedness can be axiomatized in ...

**5**

votes

**0**answers

411 views

### Natural models of graphs?

Motivation
I want to capture the notion of natural models of finite graphs: How can natural predicates and natural relations on a given natural base class $D$ be defined? If this succeeds the ...