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As stated in Woodin, Davis, and Rodriguez - The HOD dichotomy , a longstanding open problem in set theory is …
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Inner model theorists use the word "canonical" to …
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I know that $\text{ZFC}$ cannot prove the consistency of $\text{ZFC} + \neg \text{CH}$ through inner models, since $\te…
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If $0^\#$ exists, then there is some ordinal $\alpha…
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I've read several places that L, the constructible universe, is the least canonical inner model . Grigor Sargsyan explain…
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Canonical inner models $M$ are definable witho…
UCB Mathematics
https://math.berkeley.edu/~steel/talks/jensenmeet.pdf
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Inner Model Theory
WebExtender Models and Woodin Cardinals We summarize the progress of inner model theory from 1978 to the present. Mitchell (1974,1978) discovered what is probably the general …
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  6 I. An Outline of Inner Model Theory model. The reader can ﬁnd in [15] an …
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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 …
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An Outline of Inner Model Theory | Request PDF - …
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[0711.0680] The strength of the Inner Model Hypothesis - …
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A “paradox” about the inner model problem - MathOverflow
WebOct 25, 2020 · As stated in Woodin, Davis, and Rodriguez - The HOD dichotomy, a longstanding open problem in set theory is to construct a canonical inner model for …
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https://mathoverflow.net/questions/356597/inner...
set theory - Inner models with all sets generic - MathOverflow
WebApr 4, 2020 · Inner models with all sets generic. Ask Question. Asked 4 years, 1 month ago. Modified 4 years, 1 month ago. Viewed 325 times. 6. Question: Under large cardinal …
Springer
https://link.springer.com/chapter/10.1007/978-1-4020-5764-9_20
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 …
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Canonical Inner Models
Publish Year:2010
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https://mathoverflow.net/questions/322462/does...
lo.logic - Does inner model theory seek canonical models for large ...
WebFeb 4, 2019 · A remarkable result is that given an ordinal κ κ, if there is a model L[U] L [ U] in which κ κ is measurable and U U is a normal measure on κ κ, then there is exactly one …
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What is inner model theory?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 building minimal and canonical models for large cardinals has been used to calibrate lower bounds of set-theoretic statements.
An exceptional review about inner model theory
blogs.ams.org
What is an inner model of a set theory?In set theory, a branch of mathematical logic, an inner model 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 . Let L = ⟨∈⟩ be the language of set theory.
Inner model - Wikipedia
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How are inner models constructed?Inner models in the papers discussed above are typically constructed via a procedure called the full backgrounded construction. This means the extenders giving rise to the model L[ E]~ come from extenders in V (and these in turn exist because one assumes an appropriate large cardinal hypothesis holds in V ).
A BRIEF ACCOUNT OF RECENT DEVELOPMENTS IN INNER MODEL TH…
math.unt.edu
What is Godel's inner model theory?A main theme in inner model theory after Godel's work and Scott's result is the search for canonical inner models that can accommodate large cardinals beyond those accommodated by L. This is sometimes known as the Godel program. An immediate target is a measurable cardinal.
A BRIEF ACCOUNT OF RECENT DEVELOPMENTS IN INNER MODEL TH…
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https://math.unt.edu/~ntrang/IMTre.pdf
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A BRIEF ACCOUNT OF RECENT DEVELOPMENTS IN …
WebThe goal of this survey paper is to give an overview of recent developments in inner model theory. We discuss several most important questions in the eld and relevant work …
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cuny.edu
http://faculty.baruch.cuny.edu/aapter/papers/innermodels.pdf
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INNER MODELS WITH LARGE CARDINAL FEATURES …
WebARTHUR W. APTER, VICTORIA GITMAN, AND JOEL DAVID HAMKINS. Abstract. We construct a variety of inner models exhibiting features usually obtained by forcing over …
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arXiv.org
https://arxiv.org/pdf/2007.10766.pdf
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Inner Models from Extended Logics: Part 2∗ - arXiv.org
WebWe introduce a new inner model C(aa) arising from stationary logic. We show that assuming a proper class of Woodin cardinals, or alternatively MM++, the regular …
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Springer
https://link.springer.com/content/pdf/10.1007/978-1-4020-5764-9_18.pdf
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17. Beginning Inner Model Theory - Springer
Web1452 Mitchell/Beginning Inner Model Theory The main content of the sentence “V = L” is the statement ∀x∃α∃y (y = Lα & x ∈ L α).See Jech [14, Lemma 13.17] for a proof of …
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Publish Year:2010
William J. Mitchell
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https://cc-lecture.readthedocs.io/en/latest/cc_models.html
5. CC models and comments — CC_lecture 1.0 documentation
Web5. CC models and comments ¶. 5.1. Standard CC models ¶. With the equations that we have presented in the previous section, the standard models of CC theory can be easily …
Mathematics Stack Exchange
https://math.stackexchange.com/questions/3790795/...
$\\neg \\text{CH}$ within an inner model - Mathematics Stack …
WebAug 14, 2020 · There is an inner model of L[0#] L [ 0 #] in which GCH G C H fails on a proper class. Of course, since a lot of "very complicated" forcings in L L are still all …
What determines when an inner model is "canonical"?
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De Gruyter
https://www.degruyter.com/document/doi/10.1515/...
Inner Models and Large Cardinals - De Gruyter
WebSep 6, 2011 · This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties …
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https://arxiv.org/pdf/2103.13961.pdf
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GabrielGoldberg arXiv:2103.13961v2 [math.LO] 2 Nov 2021
WebMuch of the theory of large cardinals beyond a measurable cardinal concerns the structure of elementary embeddings of the universe of sets into inner models. This paper seeks …
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Inner model theory - Apeirology Wiki
WebInner model theory is the study of the "fine structure theory" and construction of inner models, proper class -sized models of ZFC which satisfy the existence of large …
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Wikipedia
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Inner model - Wikipedia
WebIn set theory, a branch of mathematical logic, an inner model [1] 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 …
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