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Superstability in simple finitary AECs

Tapani Hyttinen, Meeri Kesälä (2007)

Fundamenta Mathematicae

We continue the study of finitary abstract elementary classes beyond ℵ₀-stability. We suggest a possible notion of superstability for simple finitary AECs, and derive from this notion several good properties for independence. We also study constructible models and the behaviour of Galois types and weak Lascar strong types in this context. We show that superstability is implied by a-categoricity in a suitable cardinal. As an application we prove the following theorem: Assume that ( , ) is a simple, tame,...

The isomorphism relation between tree-automatic Structures

Olivier Finkel, Stevo Todorčević (2010)

Open Mathematics

An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that...

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Roman Kossak (1984)

Fundamenta Mathematicae

When is the orbit algebra of a group an integral domain ? Proof of a conjecture of P.J. Cameron

Maurice Pouzet (2008)

RAIRO - Theoretical Informatics and Applications

Cameron introduced the orbit algebra of a permutation group and conjectured that this algebra is an integral domain if and only if the group has no finite orbit. We prove that this conjecture holds and in fact that the age algebra of a relational structure R is an integral domain if and only if R is age-inexhaustible. We deduce these results from a combinatorial lemma asserting that if a product of two non-zero elements of a set algebra is zero then there is a finite common tranversal of their...

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