Unformatted text preview: A , B are ﬁnitely generated substructures of M and h ∶ A → B is an isomorphism, then there is an automorphism h of M with h ± h . Show that ( Q , <) is ultrahomogeneous. The same proof should also work to show that ( R , <) is ultrahomogeneous. 7. For a signature τ , a τsentence is a τformula that does not have free variables. For τstructures A , B , we write A ≡ B if for every τsentence φ , A ² φ ⇐⇒ B ² φ . (a) Show that there is a τ groupsentence φ such that M ² φ ⇐⇒ M ³ Z ´ 2 Z . (b) More generally, let τ be a ﬁnite signature and A be a ﬁnite τstructure. Show that there is a τsentence φ such that for any τstructure B , B ² φ ⇐⇒ B ³ A . In particular, B ≡ A ⇐⇒ B ³ A . 1 isomorphism with itself...
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 Fall '08
 Solecki,S
 Logic, Vector Space, Model theory, Abelian group, Isomorphism, Define appropriate signatures

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