Unidimensinality (Dimensionality of the Latent Space)
Local Independence - Local independence is the underlying assumption of latent variable models. The observed items are conditionally independent of each other given an individual score on the latent variable(s). This means that the latent variable explains why the observed items are related to one another.
Monotonicity - logistic IRT models assume a monotonically increasing functions (as trait level increases, so does the probability of endorsing an item).