Vol. 44, No. 1, 1973

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Automorphisms definable by formulas

John Grant

Vol. 44 (1973), No. 1, 107–115

The group of definable automorphisms of a structure A is denoted by (A). The following theorem is used to discover the group of definable automorphisms of various structures: If A has finite type and A B then (A) ≡ℋ(B). It is also shown that every group may be represented as the group of definable automorphisms of some structure. Definable automorphisms are then investigated in infinitary languages. Finally the notion of normal submodel is introduced in analogy to the notion of normal subgroup with definable automorphisms playing the role of inner automorphisms.

Mathematical Subject Classification 2000
Primary: 02H05
Secondary: 20A10, 02H15
Received: 14 July 1971
Published: 1 January 1973
John Grant