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WQO and BQO theory in subsystems of second order arithmetic

Published online by Cambridge University Press:  31 March 2017

Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Publisher: Cambridge University Press
Print publication year: 2005

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References

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[28] Eric C., Milner, Basic wqo- and bqo-theory,Graphs and order (Ivan Rival, editor), D. Reidel, Dordrecht, 1985, pp. 487–502.
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[31] C. St. J. A., Nash-Williams, On better-quasi-ordering transfinite sequences,Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64 (1968), pp. 273–290.
[32] Hans, Jürgen Prömel and Bernd, Voigt, From wqo to bqo, via Ellentuck's theorem,DiscreteMathematics, vol. 108 (1992), no. 1-3, pp. 83–106.
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[35] Diana, Schmidt, Well-partial orderings and their maximal order types, Habilitationschrift, Heidelberg University, 1979.
[36] Kurt, Schütte and Stephen G., Simpson, Ein in der reinen Zahlentheorie unbeweisbarer Satz über endliche Folgen von natürlichen Zahlen,Archiv für Mathematische Logik und Grundlagenforschung, vol. 25 (1985), no. 1-2, pp. 75–89.
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[39] Stephen G., Simpson, Bqo-theory and Fraïssé's conjecture, Chapter 9 of [23].
[40] Stephen G., Simpson, Nonprovability of certain combinatorial properties of finite trees, Harvey Friedman 's research on the foundations of mathematics (L. A., Harrington, M. D., Morley, A., Ščedrov, and S. G., Simpson, editors), North-Holland, Amsterdam, 1985, pp. 87–117.
[41] Stephen G., Simpson (editor), Logic and combinatorics, American Mathematical Society, Providence, R.I., 1987.
[42] Stephen G., Simpson, Ordinal numbers and the Hilbert basis theorem,The Journal of Symbolic Logic, vol. 53 (1988), no. 3, pp. 961–974.
[43] Stephen G., Simpson, Subsystems of second order arithmetic, Springer-Verlag, Berlin, 1999.
[44] Stéphan, Thomassé, On better-quasi-ordering countable series-parallel orders, Transactions of the American Mathematical Society, vol. 352 (2000), no. 6, pp. 2491–2505.
[45] Carsten Thomassen, Embeddings and minors,Handbook of combinatorics, vol. 1 (R. L., Graham, M., Grötschel, and L., Lovász, editors), Elsevier Science, Amsterdam, 1995, pp. 301–349.

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