Linear Orders

Extending Partial Orders to Dense Linear Orders

Cofinalities of Linear Orders

Adding linear orders

We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an ω-stable NDOP theory for which every expansion by a linear ord...

Epimorphisms Between Linear Orders

We study the relation on linear orders induced by order preserving surjections. In particular we show that its restriction to countable orders is a bqo.

Automatic Linear Orders

We study model-theoretic properties of automatic linear orders, in particular issues of categoricity and suborder complexity. We prove that the growth rate of the domain of a presentation of a linear order dictates the complexity. These results highlight key similarities and differences between automatic structures and other structures of effective mathematics.