I'm studying for a Logic exam and I'm currently working through past paper. However I'm finding it difficult to understand the following question.
I have been asked to:
Construct $L$-sentences formalizing the following:
i) $R(x, y)$ is a linear order with left endpoint $b$ and right endpoint $c$;
ii) $f(x)$ is a injective (i.e. one-to-one) function which has exactly two objects which bear $R(x, y)$ to $b$ in its range.
And to then:
Construct a model whose domain contains four objects in which the sentences i) and ii) you constructed are satisfied.
I'm finding it difficult to find such a module though. $b$ is a left endpoint, so surely there cannot be two objects with bear $R(x, y)$ to $b$. The two sentences seem to contradict each other, and I don't know how to construct such a model.
Thanks for the help.