Excitation of ensembles of climbing fibers—the axons of olivary neurons — in the cerebellum is predicted on the basis of observations of climbing fiber tactile receptive fields. Each stimulus excites an ensemble of climbing fibers, called its image. When receptive fields are eliminated by inhibition, injury, or the functional state of the circuit, the image poset can change. Four maps are explored: the map from the poset of all simultaneous stimulus arrays to the poset of excited ensembles, a map in the reverse direction, the map from the poset of all stimulus sequences of a given number to ensemble response, and a map in the reverse direction. The map from excitation to response is complicated by the oscillatory tendency of climbing fibers, by both phasing and response spike number. The central question motivating the study is to what extent climbing fiber activity allows discrimination of stimuli, either in simultaneous arrays or in sequences of arrays. The question is addressed by predicting equivalence classes, first on the basis of excitation of cells in the inferior olive and then on the basis of response in the climbing fibers to which they give rise. The paper provides a mechanism for climbing fibers to behave as event detectors, assuming an oscillatory behavior of inferior olive cells. It also provides another example of the combination of continuous and discrete aspects of nervous system function.