A *mouse* is, in general, a structure of the form $(J_{\alpha}^{E},\in,E)$ (see [[Jensen's hierarchy]]) where $E$ is a sequence of [[Filter|ultrafilters]] or [[Extenders|extenders]], satisfying some properties. The important property is *iterability* - the ultrafilters/extenders of $E$ can be used to form iterated ultrapowers, which are well-founded. Usually one first defines the notion of a *pre-mouse*, and then a mouse is an iterable pre-mous. The exact definition depends on the context - what level of the large cardinal hierarchy is of interest - so there are different notions of mouse. Some examples: - [[Jensen - Measures of Order Zero#2. Mice]] - [[Steel - An Outline of Inner Model Theory]]