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- W2017473860 abstract "The theorem introduced here provides a sufficient condition for an axiomatic class to be elementary. It resulted from consideration of a definability problem in , but is introduced in a less specific context and accompanied by applications to . As in [La, 1], [La, 2], a reflexive, transitive binary relation R on a nonempty set S will be called a quasi-ordering or q.o. of S . A set of pairwise incomparable elements of S is an antichain and a subset of S linearly ordered by R is a chain . A chain { S i : i ∈ ω} with i > j if and only if ( s i Rs j ∧ ¬ s j RS i ) will be called an infinite descending chain . If S has no infinite antichains nor any infinite descending chains, S is well quasi-ordered by R , and is called a well quasi-ordering or w.q.o. Any subset of a w.q.o. is a w.q.o. An element s of a q.o. S is minimal in S if ∀ t ∈ S ( tRs → sRt ). A subset S ′ of S is a foundation for S if ∀ t ∈ S ∃ s ∈ S ′( sRt )." @default.
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- W2017473860 date "1977-06-01" @default.
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- W2017473860 title "Definability in well quasi-ordered sets of structures " @default.
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- W2017473860 doi "https://doi.org/10.2307/2272132" @default.
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