Corrigendum to The complexity of plane hyperbolic incidence geometry is

摘要

In [1], on page 280, the last paragraph of Section 4 contains a mistake. The models K(R, n) do not form an ascending chain, given that K(R, n) is not a submodel of K(R, n + 1) when individuals are lines and the only predicate is 內. However, the first line of that last paragraph is correct: the theories do not admit axiom systems. The ascending chain of models is none other than the chain constructed in Section 2, namely the one consisting of the models An, with lines as variables and as predicate. As line-models with concurrency, they no longer form an ascending .1-chain, but they still form an ascending chain of models, and the union, A, is not a model of our geometry.