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Well-quasi-orderings and sets of finite sequences

  • Richard Laver (a1)

Extract

Section 1 contains a list of the facts about well-quasi-orderings (wqo's) which were established in (1), (4), (7), (10), and (13), with proofs given except for the last three theorems. The theory of well-quasi-orderings is a precursor to Nash–Williams' theory of better-quasi-orderings (10, 11, 12, 6, 7). Section 1 of this paper may be viewed as a beginning to Section 1 of a forthcoming paper, in which an explication of bqo theory is given.

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(1)Higman, G.Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2 (1952), 326336.
(2)Jenkyns, T. A. and Nash-Williams, C. ST J. A.Counter examples in the theory of wellquasi-ordered sets. Univ. of Waterloo (minimeographed).
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(10)Nash-Williams, C.ST J. A. On well-quasi-ordering tranafinite sequences. Proc. Cambridge Philos. Soc. 61 (1965), 3339.
(11)Nash-Williams, C.ST J. A. On well-quasi-ordering infinite trees. Proc. Cambridge Philos. Soc. 61 (1965), 697720.
(12)Nash-Williams, C. ST J. A.On better-quasi-ordering transfinite sequences. Proc. Cambridge Philos. Soc. 64 (1968), 273290.
(13)Rado, R.Partial well ordering of sets of vectors. Mathematika 1 (1954), 8995.
(14)Watkins, M. E.A theorem on Tait colorings with an application to the generalized Petersen graphs. J. Combinatorial Theory 6 (1969), 152164.

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