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The regular inverse Galois problem over non-large fields

Jochen Koenigsmann (2004)

Journal of the European Mathematical Society

By a celebrated theorem of Harbater and Pop, the regular inverse Galois problem is solvable over any field containing a large field. Using this and the Mordell conjecture for function fields, we construct the first example of a field K over which the regular inverse Galois problem can be shown to be solvable, but such that K does not contain a large field. The paper is complemented by model-theoretic observations on the diophantine nature of the regular inverse Galois problem.

The smallest common extension of a sequence of models of ZFC

Lev Bukovský, Jaroslav Skřivánek (1994)

Commentationes Mathematicae Universitatis Carolinae

In this note, we show that the model obtained by finite support iteration of a sequence of generic extensions of models of ZFC of length ω is sometimes the smallest common extension of this sequence and very often it is not.

The structure of superilat graphs

A. Ivanov (1993)

Fundamenta Mathematicae

We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.

The theory of dual groups

A. Mekler, G. Schlitt (1994)

Fundamenta Mathematicae

We study the L ∞ , w -theory of sequences of dual groups and give a complete classification of the L ∞ , w -elementary classes by finding simple invariants for them. We show that nonstandard models exist.

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