Definition: A σ-automorphism of a σ-structure A is just a σ-isomorphism h : A → A. The identity map idA is a σ-automorphism of A, but there are typically many other σ-automorphisms. A σ-structure is called rigid if it has no σ-automorphisms other than the identity. Show that the structures N := (ℕ,0, S,+,·) and Q := (ℚ,0,1,+,·) are rigid. Here, the symbol S is interpreted as the successor operation n ↦ n + 1 and all other symbols are with their standard interpretations.
Definition: A σ-automorphism of a σ-structure A is just a σ-isomorphism h : A → A. The identity map idA is a σ-automorphism of A, but there are typically many other σ-automorphisms. A σ-structure is called rigid if it has no σ-automorphisms other than the identity. Show that the structures N := (ℕ,0, S,+,·) and Q := (ℚ,0,1,+,·) are rigid. Here, the symbol S is interpreted as the successor operation n ↦ n + 1 and all other symbols are with their standard interpretations.
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter12: Adding Functionality To Your Classes
Section12.5: Virtual Functions
Problem 5E
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Definition: A σ-automorphism of a σ-structure A is just a σ-isomorphism h : A → A. The identity map idA is a σ-automorphism of A, but there are typically many other σ-automorphisms.
A σ-structure is called rigid if it has no σ-automorphisms other than the identity. Show that the structures N := (ℕ,0, S,+,·) and Q := (ℚ,0,1,+,·) are rigid. Here, the symbol S is interpreted as the successor operation n ↦ n + 1 and all other symbols are with their standard interpretations.
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