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Well-Quasi Orders in Computation, Logic, Language and Reasoning pp 189–219Cite as

The Reverse Mathematics of wqos and bqos

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Part of the book series: Trends in Logic ((TREN,volume 53))

Abstract

In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced theorems. The classification from the reverse mathematics viewpoint of both kinds of results provides interesting challenges, and we cover also recent advances on some long standing open problems.

I thank Marta Fiori Carones and Emanuele Frittaion who carefully read an earlier draft of this paper.

Research partially supported by PRIN 2012 Grant “Logica, Modelli e Insiemi”.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100, Udine, Italy

    Alberto Marcone

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  1. Alberto Marcone
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Correspondence to Alberto Marcone .

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Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, Verona, Italy

    Peter M. Schuster

  2. Department of Computer Science, Swansea University, Swansea, UK

    Monika Seisenberger

  3. Vakgroep Wiskunde, Ghent University, Ghent, Belgium

    Andreas Weiermann

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Marcone, A. (2020). The Reverse Mathematics of wqos and bqos. In: Schuster, P., Seisenberger, M., Weiermann, A. (eds) Well-Quasi Orders in Computation, Logic, Language and Reasoning. Trends in Logic, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-30229-0_8

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