  Counterfactuals are conditional statements describing consequences of states
of affairs that might not have occurred. Ceteris paribus counterfactuals take
into account specific conditions which hold at the actual state of affairs, and
which ought to be kept unchanged throughout the evaluation. Inspired by the
approach of Girard and Triplett, we define ceteris paribus conditionals as
dynamic operators over (weakly) centered sphere models. We introduce three ways
of evaluating the operators, by updating sphere models based on ceteris paribus
sets of formulas. Our approach features two main novelties: on the one hand, we
define our ceteris paribus conditionals as proper dynamic operators, thus
allowing for iterated evaluations. On the other hand, when updating the worlds
within a system of sphere we additionally take into account a notion of
'significance' of the formulas that ought to be kept unchanged. We discuss the
relations of our model updates with other prioritisations introduced in the
literature, and show completeness of the set of valid formulas in the updated
centered (resp. weakly centered) sphere models with respect to Lewis'
axiomatization of the conditional logic VC (resp. VW).
