Inner CC Models

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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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UCB Mathematics
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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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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 …
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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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What is basic inner model theory?L contained in Jensen’s paper . We shall present basic inner model theory in what is roughly the greatest generality in which it is currently known. This means that the theory we shall outline applies to extender models which may satisfy large cardinal hypotheses as strong as “There is a Woodin cardinal which is a limit of Woodin cardinals”.
An Outline of Inner Model Theory - University of California, Berkeley
math.berkeley.edu
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 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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Department of Mathematics
https://math.unt.edu/~ntrang/IMTre.pdf
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A BRIEF ACCOUNT OF RECENT DEVELOPMENTS IN …
WebA BRIEF ACCOUNT OF RECENT DEVELOPMENTS IN INNER MODEL THEORY. NAM TRANG Department of Mathematics University of North Texas, Denton, TX, USA Email: …
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De Gruyter
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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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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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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 City Challenge Chicago – A 501c3 Nonprofit Organization
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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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David Hamilton | Artnet
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Nature
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Small-scale layered structures at the inner core boundary
WebThe inner core boundary (ICB), wherethe crystallization takes place, holds the key to understandingthegrowth,thethermalandcompositionalevolutionof...
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N-Scale Model of Pioneer Oil Refinery - scvhistory.com
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Classical Conversations
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