Inner CC Models

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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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What is inner model theory?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 models to determinacy, large cardinals, and descriptive set theory. Despite the name, it is considered more a branch of set theory than of model theory .
Inner model theory - Wikipedia
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What are the standard models of CC theory?With the equations that we have presented in the previous section, the standard models of CC theory can be easily defined. Basically a given CC model is defined by the truncation level of the cluster operator (a bit like in the CI models).
5. CC models and comments — CC_lecture 1.0 documentation - Read th…
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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…
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What is a smaller class of inner models?One can obtain a deeper analysis of a smaller class of inner models by restricting to models satisfying at most “There is a strong cardinal” (and therefore having only 1 3 reals). The basic theory of this smaller class of models is significantly simpler, especially with regard to the structure of the iterated ultrapowers it uses.
An Outline of Inner Model Theory - University of California, Berkeley
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An Outline of Inner Model Theory - University of California, …
E = { (a, x) | a ∈ [λ]<ω ∧ x ⊆ [κ]|a| ∧ x ∈ M ∧ a ∈ j(x)}.
x ∈ Ea ⇔ xac ∈ Ec.
E (f)(a),
Eα ∩ ([η]<ω × JE ) ∈ JE
Proof. Fix ξ < (κ+)JE
f ∈ JE and f : JE → JE
4. The Dodd-Jensen Lemma
6.1. Kc constructions
R ∩ X = R∗.
L(R) |= ∃vσ[y,α ],
8.1 Definition.
J Q
A ∈ x ⇒ ∃α < κ(C \ α ⊆ A).
f : κ → κ ∧ f ∈ M}.
For this implies that the union over x of the x is just the ω-closed un-bounded filter on κ. Since every A ⊆ κ is in some HODx, this union is an ultrafilter. Since every f : κ → κ is in some HODx, that ultrafilter is normal, and hence κ-complete. We now construct the desired generating set for x. Let us assume x = 0, so that we can use our earlier ...
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(PDF) Descriptive inner model theory - ResearchGate
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An Outline of Inner Model Theory | SpringerLink
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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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Wikipedia
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Inner model theory - Wikipedia
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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 models to determinacy, large cardinals, and descriptive set theory. Despite the name, it is considered more a branch of set theory than of model theory.
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https://cc-lecture.readthedocs.io/en/latest/cc_models.html
5. CC models and comments — CC_lecture 1.0 documentation
WebStandard CC models ¶. With the equations that we have presented in the previous section, the standard models of CC theory can be easily defined. Basically a given CC model is …
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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Inner Model Theory
Canonical Inner Models
Publish Year:2010
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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Inner Model Theory
Inner Models and Large Cardinals
Set Theory
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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Inner Model Theory
Publish Year:2010
William J. Mitchell
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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Inner Model Theory
Set Theory
MathOverflow
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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Inner Model Theory
Canonical Inner Models
MathOverflow
https://mathoverflow.net/questions/374835/a...
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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cuny.edu
http://faculty.baruch.cuny.edu/aapter/papers/innermodels.pdf
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INNER MODELS WITH LARGE CARDINAL FEATURES …
WebINNER MODELS WITH LARGE CARDINAL FEATURES USUALLY OBTAINED BY FORCING. ARTHUR W. APTER, VICTORIA GITMAN, AND JOEL DAVID HAMKINS. …
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Wikipedia
https://en.wikipedia.org/wiki/Category:Inner_model_theory
Category:Inner model theory - Wikipedia
WebInner 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 …
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Inner Model Theory
Inner Models and Large Cardinals
Mathematics Stack Exchange
https://math.stackexchange.com/questions/54099
$A^\\#$ and inner models - Mathematics Stack Exchange
WebSo, suppose $M$ is an inner model and $M$ thinks that $A^\sharp$ exists. Then $M$ sees an elementary embedding of $L[A]$ into itself. This is clearly seen in $V$ as well. So …
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X in Set Theory
Mathematics Stack Exchange
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What determines when an inner model is "canonical"?
WebSorted by: +100. Canonical inner models M are definable without parameters and, in fact, "locally" definable, that is, there is a formula ψM such that M = {x ∣ ψM(x)}. (Of course, …
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Canonical Inner Models
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Definition of Canonical Model
Springer
https://link.springer.com/article/10.1007/s11214-020-00748-w
The NC-CC Isotope Dichotomy: Implications for the Chemical
WebNov 17, 2020 · The NC groups purportedly originated in the inner disk, and the CC groups were derived from the outer disk, where the NC and CC regions of the disk may have …
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Katherine R. Bermingham, Evelyn Füri, Katharina Lodders, Bernard Marty
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Inner Classifier-Free Guidance and Its Taylor Expansion for...
WebJan 16, 2024 · This approach involves utilizing a single model to jointly optimize the conditional score predictor and unconditional score predictor, eliminating the need for …
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Internal Working Models of Attachment - Simply Psychology
WebNov 29, 2023 · Saul Mcleod, PhD. Updated on. November 29, 2023. Reviewed by. Olivia Guy-Evans, MSc. Key Takeaways. Attachment theory posits that individuals develop …
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