Kellerman, RuaanGoranko, Valentin2023-01-302023-01-302021-09Kellerman, R. & Goranko, V. (2021). Approximating trees as coloured linear orders and complete axiomatisations of some classes of trees. The Journal of Symbolic Logic, 86(3), 1035-1065. doi:10.1017/jsl.2021.40.0022-4812 (print)1943-5886 (online)10.1017/jsl.2021.40https://repository.up.ac.za/handle/2263/89008We 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.en© Association for Symbolic Logic 2021AxiomatisationFirst-order theoryTreeColoured linear orderPostprint Article