What's an example of an ordered set other than R that obeys the first 3 Suslin conditions?
Open link in next tab
Suslin's problem - Wikipedia
https://en.wikipedia.org/wiki/Suslin%27s_problem#Formulation
https://en.wikipedia.org/wiki/Suslin%27s_problem#Formulation
I think you could just take an open interval in the order topology and then create a collection by turning the first dimension into a parameter. IIANM for each value of the parameter you'd get an open set, they'd be pairwise disjoint, and there'd be uncountably many of them.