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APPROXIMATING TREES AS COLOURED LINEAR ORDERS AND COMPLETE AXIOMATISATIONS OF SOME CLASSES OF TREES

Part of: Ordered sets Model theory General logic

Published online by Cambridge University Press:  08 June 2021

RUAAN KELLERMAN  and
VALENTIN GORANKO
RUAAN KELLERMAN
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS UNIVERSITY OF PRETORIAPRETORIA, SOUTH AFRICAE-mail:[email protected]
VALENTIN GORANKO
Affiliation:
DEPARTMENT OF PHILOSOPHY STOCKHOLM UNIVERSITYSTOCKHOLM, SWEDEN and SCHOOL OF MATHEMATICS (VISITING PROFESSORSHIP) UNIVERSITY OF THE WITWATERSRAND JOHANNESBURG, SOUTH AFRICA E-mail:[email protected]
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Abstract

We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of the four classes of trees mentioned above.

Keywords

axiomatisationfirst-order theorycoloured linear ordertree

MSC classification

Primary: 03C07: Basic properties of first-order languages and structures
Secondary: 03B10: Classical first-order logic 03C64: Model theory of ordered structures; o-minimality 03C68: Other classical first-order model theory 06A05: Total order 06A06: Partial order, general
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 3 , September 2021 , pp. 1035 - 1065
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Copyright
© Association for Symbolic Logic 2021

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References

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