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On elementarily κ-homogeneous unary structures
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Greg Oman
Published/Copyright:
March 26, 2010
Abstract
Let L be a first-order language with equality and let 𝔘 be an L-structure of cardinality κ. If ℵ0 ≤ λ ≤ κ, then we say that 𝔘 is elementarily λ-homogeneous iff any two substructures of cardinality λ are elementarily equivalent, and λ-homogeneous iff any two substructures of cardinality λ are isomorphic. In this note, we classify the elementarily λ-homogeneous structures (A, ƒ) where ƒ : A → A is a function and λ is a cardinal such that ℵ0 ≤ λ ≤ |A|. As a corollary, we obtain a complete description of the Jónsson algebras (A, ƒ), where ƒ : A → A.
Received: 2009-05-09
Revised: 2009-09-10
Published Online: 2010-03-26
Published in Print: 2011-July
© de Gruyter 2011
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Articles in the same Issue
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