Mouse (set theory)
In set theory, a mouse is a small model of (a fragment of) Zermelo–Fraenkel set theory with desirable properties. The exact definition depends on the context. In most cases, there is a technical definition of "premouse" and an added condition of iterability (referring to the existence of wellfounded iterated ultrapowers): a mouse is then an iterable premouse. The notion of mouse generalizes the concept of a level of Gödel's constructible hierarchy while being able to incorporate large cardinals.
- Dodd, A.; Jensen, R. (1981). "The core model". Ann. Math. Logic. 20 (1): 43–75. MR 0611394.
- Jech, Thomas (2003). Set Theory. Springer Monographs in Mathematics (Third Millennium ed.). Berlin, New York: Springer-Verlag. ISBN 978-3-540-44085-7. Zbl 1007.03002.
- Mitchell, William (1979). "Ramsey cardinals and constructibility". J. Symbolic Logic. 44 (2): 260–266. MR 0534574.