Recursive linear orders with recursive successivities |
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Authors: | Michael Moses |
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Institution: | Department of Mathematics, Western Illinois University, Macomb, IL 61455, USA |
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Abstract: | A successivity in a linear order is a pair of elements with no other elements between them. A recursive linear order with recursive successivities is recursively categorical if every recursive linear order with recursive successivities isomorphic to is in fact recursively isomorphic to . We characterize those recursive linear orders with recursive successivities that are recursively categorical as precisely those with order type k1+g1+k2+g2+…+gn-1+kn where each kn is a finite order type, non-empty for i?{2,…,n-1} and each gi is an order type from among {ω,ω*,ω+ω*}∪{k·η:k<ω}. |
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