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See all on WikipediaInner model theory - Wikipedia
In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive subsets or subclasses of the von Neumann universe V, or sometimes of a generic extension of V. Inner model theory studies the relationships of these … See more
• The class of all sets is an inner model containing all other inner models.
• The first non-trivial example of an inner model was the constructible universe L developed by Kurt Gödel. Every model M of ZF has an inner model L … See moreOne important use of inner models is the proof of consistency results. If it can be shown that every model of an axiom A has an inner model satisfying axiom B, then if A is See more
Wikipedia text under CC-BY-SA license WebI. An Outline of Inner Model Theory John R. Steel 1. Introduction This article is an exposition of the theory of canonical inner models for large cardinal hypotheses, or …
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Inner Model Theory
WebInner Model Theory. John R. Steel. University of California, Berkeley. Humboldt University, Berlin. October 2001. Large Cardinal Hypotheses. The ordinals are 0, 1, 2, ..., ω, ω + 1, …
Inner model - Wikipedia
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.Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 3 mins
The Continuum Hypothesis - Stanford Encyclopedia of Philosophy
WebMay 22, 2013 · 6. The Ultimate Inner Model. Inner model theory aims to produce “L-like” models that contain large cardinal axioms. For each large cardinal axiom Φ that has …
WebBeginning Inner Model Theory. William J. Mitchell. Contents. The Constructible Sets . . . . . . . . . . . . . . . . . 1451. 1.1 Relative Constructibility . . . . . . . . . . . . . . . . 1453. 1.2 …
An Outline of Inner Model Theory | SpringerLink
WebDec 10, 2009 · This paper outlines the basic theory of canonical inner models satisfying large cardinal hypotheses. It begins with the definition of the models, and their fine …
WebA BRIEF ACCOUNT OF RECENT DEVELOPMENTS IN INNER MODEL THEORY. NAM TRANG Department of Mathematics University of North Texas, Denton, TX, USA Email: …
Beginning Inner Model Theory | SpringerLink
WebDec 10, 2009 · Beginning Inner Model Theory. Chapter. First Online: 10 December 2009. pp 1449–1495. Cite this chapter. Download book PDF. William J. Mitchell. 5185 …
WebDescriptive inner model theory is the theory behind the approach to the inner model prob-lem described above. Its main technical goal is to construct canonical models of …
An exceptional review about inner model theory
WebAug 27, 2016 · Inner model theory has both test questions that it tries to resolve and unexplained phenomena that it tries to elucidate. The inner model-theoretic approach to …
WebAbstract. The standard comparison lemma of inner model theory is de cient, in that it does not in general produce a comparison of all the relevant inputs. How two mice compare …
WebLarge Cardinals, Inner Models and Determinacy: an introductory overview. P.D. Welch. School of Mathematics, University of Bristol, England, Isaac Newton Institute for …
Independence and Large Cardinals - Stanford Encyclopedia of …
WebApr 20, 2010 · The branch of set theory known as inner model theory is devoted to the construction of such “L-like” models for stronger and stronger large cardinal axioms. In …
WebDescriptive inner model theory is the theory behind the approach to the inner model problem described above. Its main technical goal is to construct canonical models of …
WebSet-theoretic Geology, the Ultimate Inner Model, and New Axioms Justin William Henry Cavitt (860) 949-5686 [email protected] Advisor: W. Hugh Woodin Harvard …
Inner Models and Large Cardinals - De Gruyter
WebSep 6, 2011 · About this book. This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large …
[PDF] An Outline of Inner Model Theory | Semantic Scholar
WebAn Outline of Inner Model Theory. J. Steel. Published 2010. Mathematics. This paper outlines the basic theory of canonical inner models satisfying large cardinal hypotheses. …
Descriptive inner model theory | Bulletin of Symbolic Logic
WebThe purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model …
Deconstructing inner model theory | The Journal of Symbolic …
WebDeconstructing inner model theory. Published online by Cambridge University Press: 12 March 2014. Ralf-Dieter Schindler , John Steel and. Martin Zeman. Article. Metrics. Get …
Gabriel Goldberg - University of California, Berkeley
WebThe inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a …
MARTIN ZEMAN - University of California, Irvine
WebAug 2, 2020 · Email: [email protected]. PUBLICATIONS. INNER MODEL THEORY MEETINGS: 2016 2023. GRADUATE SUMMER SCHOOL IN SET THEORY: 2016 2015 …
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Web6 days ago · We have applied the OLS, PSM, and quantile regression models using field survey data from 261 herders in Xilin Gol, Inner Mongolia Autonomous Region for our …
John R. Steel: Online Preprints - University of California, Berkeley
WebJohn R. Steel: Online Preprints. An Outline of Inner Model Theory, in ``Handbook of Set Theory'', to appear. postscript. or pdf. with Benedikt Loewe. An Introduction to Core …
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