GetWiki
inner model
ARTICLE SUBJECTS
being →
database →
ethics →
fiction →
history →
internet →
language →
linux →
logic →
method →
news →
policy →
purpose →
religion →
science →
software →
truth →
unix →
wiki →
ARTICLE TYPES
essay →
feed →
help →
system →
wiki →
ARTICLE ORIGINS
critical →
forked →
imported →
original →
inner model
please note:
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{About|models of mathematical set theory|the standard effective temperature (SET) model |Thermal comfort#Standard effective temperature}}In set theory, a branch of mathematical logic, an inner modelDOCUMENT, Shepherdson, J.C., Inner Models for Set Theory, Journal of Symbolic Logic, 1951â53, for a theory T is a substructure of a model M of a set theory that is both a model for T and contains all the ordinals of M.- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
Definition
Let L = â¨ââ© be the language of set theory. Let S be a particular set theory, for example the ZFC axioms and let T (possibly the same as S) also be a theory in L. If M is a model for S, and N is an {{nowrap|L-structure}} such that- N is a substructure of M, i.e. the interpretation âN of â in N is âM â© N2
- N is a model of T
- the domain of N is a transitive class of M
- N contains all ordinals in M
Use
Usually when one talks about inner models of a theory, the theory one is discussing is ZFC or some extension of ZFC (like ZFC + "a measurable cardinal exists"). When no theory is mentioned, it is usually assumed that the model under discussion is an inner model of ZFC. However, it is not uncommon to talk about inner models of subtheories of ZFC (like ZF or KP) as well.Related ideas
Kurt Gödel proved that any model of ZF has a least inner model of ZF, the constructible universe, which is also an inner model of ZFC + GCH. There is a branch of set theory called inner model theory that studies ways of constructing least inner models of theories extending ZF. Inner model theory has led to the discovery of the exact consistency strength of many important set theoretical properties.See also
References
{{reflist}}- content above as imported from Wikipedia
- "inner model" does not exist on GetWiki (yet)
- time: 5:51pm EDT - Wed, May 01 2024
- "inner model" does not exist on GetWiki (yet)
- time: 5:51pm EDT - Wed, May 01 2024
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 23 MAY 2022
The Illusion of Choice
Culture
Culture
GETWIKI 09 JUL 2019
Eastern Philosophy
History of Philosophy
History of Philosophy
GETWIKI 09 MAY 2016
GetMeta:About
GetWiki
GetWiki
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
Biographies
GETWIKI 20 AUG 2014
GetMeta:News
GetWiki
GetWiki
© 2024 M.R.M. PARROTT | ALL RIGHTS RESERVED