In Buddhism there is no self and no soul and no permanent objects of any sort. In Christianity there is a soul that goes to heaven. Seems different but of course it is more complex. In Buddhism there is reincarnation so it is fair to ask, what gets reincarnated if there is no soul. To answer this we need to turn to process philosophy, which is an often ignored branch of western philosophy that explains Buddhist ideas on permanence using language more suited to western philosophers. The main difference is that Buddhist explanations are usually made in the pragmatic context of reducing suffering in individuals, whereas western philosophy is more about universal truth and metaphysics. Anyway, process philosophy is very unpopular because it states that nothing exists, there are only cause and effect processes. So a rock is not a rock it is rocking (this is actually how some North American First Nations languages (e.g, Cree) work). Applied to the soul it means there is no soul, there is only souling. So reincarnation occurs because souling continues after death. This can be applied equally to notions of heaven, where souling continues but not in a new body. In fact, with this notion you can have both, where after death souling continues in new bodies and elsewhere. In ancient Chinese religion the soul was believed to go to more than one place. However we have trouble thinking without permanent objects so we need them. We just need to keep in mind that they are not real. In the diamond sutra the Buddha says, there is a mountain (belief in object), there is no mountain (realization that there are no objects), there is a mountain (pragmatic use of the idea of mountain to refer to mountaining). So with the soul. The concept of the soul as an object helps us to make progress under certain conditions. But beyond that it can become poisonous, and cause people to selfishly pursue wealth and immortality in an imagined afterlife with all delusions of this life. A dogmatic adherence to the idea of no self can also be a problem, for different reasons. Tich Nhat Hanh sometimes talks about the existence of the soul and the non existence of the soul as being equal. This is because dogmatic attachment to a belief, even if the belief is of the absence of something, is still a type of permanent object, albeit a more rarified one.