REDUCTS OF STRUCTURES AND MAXIMAL-CLOSED PERMUTATION GROUPS
Copyright policy )REDUCTS OF STRUCTURES AND MAXIMAL-CLOSED PERMUTATION GROUPS
AbstractAnswering a question of Junker and Ziegler, we construct a countable first order structure which is not ω-categorical, but does not have any proper nontrivial reducts, in either of two senses (model-theoretic, and group-theoretic). We also construct a strongly minimal set which is not ω-categorical but has no proper nontrivial reducts in the model-theoretic sense.
- École Polytechnique France
- Laboratoire d'informatique France
- LABORATOIRE D'INFORMATIQUE France
- White Rose Consortium: University of Leeds; University of Sheffield; University of York United Kingdom
- University of Leeds United Kingdom
Model-theoretic algebra, Quantifier elimination, model completeness, and related topics, Mathematics - Logic, Interpolation, preservation, definability, D-relations, Categoricity and completeness of theories, Subgroups of symmetric groups, maximal closed subgroups, strongly minimal sets, FOS: Mathematics, Jordan permutation groups, Infinite automorphism groups, reducts, Logic (math.LO)
Model-theoretic algebra, Quantifier elimination, model completeness, and related topics, Mathematics - Logic, Interpolation, preservation, definability, D-relations, Categoricity and completeness of theories, Subgroups of symmetric groups, maximal closed subgroups, strongly minimal sets, FOS: Mathematics, Jordan permutation groups, Infinite automorphism groups, reducts, Logic (math.LO)
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