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UCB Mathematics
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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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A QUICK INTRODUCTION TO BASIC SET THEORY - …
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Basic Set Theory
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AN INTRODUCTION TO SET THEORY - University of …
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Lecture 7: Set Theory and Logic - Harvard University
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Inner model theory - Wikipedia
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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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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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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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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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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.
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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 …
WebDIMT uses tools from both descriptive set theory (DST) and inner model theory (IMT) to study and deepen the connection between canonical models of large cardinals and …
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MathOverflow
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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 …
A “paradox” about the inner model problem Oct 24, 2020
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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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Wikipedia
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Inner model theory - Wikipedia
WebInner 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 …
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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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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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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 …
Springer
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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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William J. Mitchell
Mathematics Stack Exchange
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$A^\\#$ and inner models - Mathematics Stack Exchange
WebSuppose $V$ is a model of $ZFC$, $A$ a set of ordinals and $M$ is a transitive inner model such that $A\in M$ and $M\models A^\#\text{ exists}$. Does that imply …
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What determines when an inner model is "canonical"?
Web8. I've read several places that L, the constructible universe, is the least canonical inner model. Grigor Sargsyan explains in his slides that L is canonical due to RL being Σ12 …
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Definition of Canonical Model
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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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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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N-Scale Model of Pioneer Oil Refinery - scvhistory.com
WebN-Scale Model of Pioneer Oil Refinery. Newhall, California. N-scale model kit of the Pioneer Oil Refinery and Andrew's Station in Newhall, developed by San Francisco architect and …
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Reflective Practice for Educators
WebBecause the intent of reflective practice is to improve the quality of professional performance, we begin our inquiry by focusing on problems of practice. There are many …
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Karen F Osterman
Reflective Practice For Educators
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Santa Susana Pacific Model Railroad
WebLocated in Simi Valley’s original Southern Pacific Railway Depot built in 1903, members of the Rancho Simi Parks Association have restored the structure to it’s original condition …
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2007 Rhoda St, Simi Valley, CA 93065 - realtor.com
WebView 11 photos for 2007 Rhoda St, Simi Valley, CA 93065, a 1 beds, 1 baths, 675 Sq. Ft. rental home with a rental price of $2500 per month. Browse property photos, details, and …
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A “paradox” about the inner model problem	Oct 24, 2020
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