Abstract
We investigate the extent to which structures consisting of sequences of forests on the same underlying set are well-quasi-ordered under embeddings.
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References
Barwise J.: Admissible Sets and Structures. Springer, Berlin (1975)
Carlson T.: Ordinal arithmetic and \({\Sigma_{1}}\) -elementarity. Arch. Math. Log. 38, 449–460 (1999)
Carlson T.: Elementary patterns of resemblance. Ann. Pure Appl. Log. 108, 19–77 (2001)
Carlson T.: Patterns of resemblance of order 2. Ann. Pure Appl. Log. 158, 90–124 (2009)
Higman G.: Ordering by divisibility in abstract algebras. Proc. Lond. Math. Soc. (Third Series).2, 326–336 (1952)
Kruskal J.B.: Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Trans. Am. Math. Soc. 95, 210–225 (1960)
Kruskal J.B.: The theory of well-quasi-orderings: a frequently discovered concept. J. Comb. Theory (A) 13, 297–305 (1972)
Laver R.: Well-quasi-orderings and sets of finite sequences. Math. Proc. Camb. Philos. Soc. 79, 1–10 (1976)
Marcone, A: On the logical strength of Nash-Williams’ theorem on transfinite sequences. In: Hodges, W., Hyland, M., Steinhorn, C., Truss, J. Logic: From Foundations to Applications, pp. 327-351. The Clarendon Press, New York (1996)
Nash-Williams C.St.J.A.: On well-quasi-ordering finite trees. Proc. Camb. Philos. Soc. 59, 833–835 (1963)
Simpson S.G.: Subsystems of Second Order Arithmetic, 2nd edn. Perspectives in Logic. Cambridge University Press, Cambridge (2010)
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Carlson, T. Generalizing Kruskal’s theorem to pairs of cohabitating trees. Arch. Math. Logic 55, 37–48 (2016). https://doi.org/10.1007/s00153-015-0457-4
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DOI: https://doi.org/10.1007/s00153-015-0457-4