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.

Mice are important ingredients of the construction of core models. The concept was isolated by Ronald Jensen in the 1970s and has been used since then in core model constructions of many authors.

This set theory-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Set theory stubs Inner model theory Wikimedia Foundation. 2010. Игры ⚽ Нужно сделать НИР? Peterhead, South Australia Controlled Bleeding Look at other dictionaries: List of set theory topics — Logic portal Set theory portal …   Wikipedia Mouse (disambiguation) — A mouse is a small rodent. Mouse may also refer to: Contents 1 People 2 Fictional characters 3 Other uses …   Wikipedia Dual inheritance theory — (DIT), also known as gene culture coevolution, was developed in the late 1970s and early 1980s to explain how human behavior is a product of two different and interacting evolutionary processes: genetic evolution and cultural evolution. DIT is a… …   Wikipedia DNA damage theory of aging — The DNA damage theory of aging proposes that aging is a consequence of unrepaired DNA damage accumulation. Damage in this context includes chemical reactions that mutate DNA and/or interfere with DNA replication. Although both mitochondrial and… …   Wikipedia Prototype Theory — is a mode of graded categorization in cognitive science, where some members of a category are more central than others. For example, when asked to give an example of the concept furniture , chair is more frequently cited than, say, stool .… …   Wikipedia Do Not Adjust Your Set — DVD cover From left to right: David Jason, Michael Palin, Eric Idle, Denise Coffey and Terry Jones. Format television comedy Starring …   Wikipedia List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium Nova (novel) — Nova   Cover of first edition (hardcover) …   Wikipedia Core model — In set theory, the core model is a definable inner model of the universe of all sets. Even though set theorists refer to the core model , it is not a uniquely identified mathematical object. Rather, it is a class of inner models that under the… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”