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- Hans Adler
- 2007

We introduce the notion of the burden of a partial type in a complete first-order theory and call a theory strong if all types have almost finite burden. In a simple theory it is the supremum of the weights of all extensions of the type, and a simple theory is strong if and only if all types have finite weight. A theory without the independence property is… (More)

- HANS ADLER, Hans Adler
- 2007

A ternary relation | between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence… (More)

- Hans Adler
- 2007

We present an updated exposition of the classical theory of complete first order theories without the independence property.

The notion of a VC-minimal theory is introduced, a slightly more general variant of C-minimality that also includes all strongly minimal or (weakly) o-minimal theories. The 1-dimensional definable sets in a VC-minimal theory have a good 'swiss cheese' representation similar to the C-minimal case. VC-minimal theories are dp-minimal; in particular they do not… (More)

- HANS ADLER, Hans Adler
- 2007

We introduce the notion of a preindependence relation between subsets of the big model of a complete first-order theory, an abstraction of the properties which numerous concrete notions such as forking, dividing, thorn-forking, thorn-dividing, splitting or finite satisfiability share in all complete theories. We examine the relation between four additional… (More)

We give a simple proof that the straightforward generalisation of clique-width to arbitrary structures can be unbounded on structures of bounded tree-width. This can be corrected by allowing fusion of elements.

We prove two results about generically stable types p in arbitrary theories. The first, on existence of strong germs, generalizes results from [3] on stably dominated types. The second is an equivalence of forking and dividing, assuming generic stability of p (m) for all m. We use the latter result to answer in full generality a question posed by Hasson and… (More)

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of cliques that occur as (topological) r-minors. We observe that this tameness notion from algorithmic graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability… (More)

- Hans Adler
- 2007

A theory with the strict order property does not eliminate hyperimaginaries. Hence a theory without the independence property eliminates hyperimaginaries if and only if it is stable. A type definable equivalence relation is an equivalence relation on tuples of a certain length (possibly infinite) which is defined by a partial type E(¯ x; ¯ y) over ∅. A… (More)

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