Inner CC Models

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UCB Mathematics
https://math.berkeley.edu/~steel/talks/jensenmeet.pdf
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Inner Model Theory
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Inner Model Theory Slogan : Associate to each large cardinal hypothesis a canonical inner model which is in some sense minimal, and whose structure can be analyzed systematically in detail. From this we get: 1. Evidence for the consistency of the large cardinal hypothesis in question. 2. Consistency strength lower bounds. For example
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(PDF) Descriptive inner model theory - ResearchGate
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An Outline of Inner Model Theory - University of California, …
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ECE 382 Fall 2018 The Internal Model Principle
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The Internal Model Principle of Control Theory - …
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Inner Models and Large Cardinals - De Gruyter
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UCB Mathematics
https://math.berkeley.edu/~steel/papers/steel1.pdf
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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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An Outline of Inner Model Theory | SpringerLink
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Inner vs Outer Model in a SEM Diagram Source: Wong (2014)
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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 to …
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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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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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MathOverflow
https://mathoverflow.net/questions/356597/inner...
set theory - Inner models with all sets generic - MathOverflow
WEBApr 4, 2020 · Every countable model $M$ of ZFC is HOD of some model of ZFC (obtained using class forcing over $M$). However, let $M_∞$ (or $M_\text{Ord}$) be the minimal …
Springer
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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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Inner Model Theory
Canonical Inner Models
Publish Year:2010
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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
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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 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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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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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
WEBThis chapter provides an introduction to the basic theory of inner models without fine structure. It assumes that the reader is familiar with G ̈odel’s class L of constructible …
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Publish Year:2010
William J. Mitchell
Beginning Inner Model Theory
arXiv.org
https://arxiv.org/pdf/1206.2712.pdf
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Descriptiveinnermodeltheory ∗† - arXiv.org
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 …
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Inner Model Theory
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Canonical Inner Models
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 Models and Large Cardinals
Springer
https://link.springer.com/chapter/10.1007/978-1-4020-5764-9_18
Beginning Inner Model Theory | SpringerLink
WEBDec 10, 2009 · This chapter provides an introduction to the basic theory of inner models of set theory, without fine structure. Section 1 begins with the basic theory of Gödel’s class …
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Set Theory
Publish Year:2010
Beginning Inner Model Theory
Wikipedia
https://en.wikipedia.org/wiki/Inner_model
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 the …
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Inner Model Theory
Axiom of Regularity
Zermelo–Fraenkel Set Theory
arXiv.org
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 …
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 uncountable …
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models-forum.net
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Fashion Land – Models Forum
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readthedocs.io
https://cc-lecture.readthedocs.io/en/latest/cc_models.html
5. CC models and comments — CC_lecture 1.0 documentation
WEBCC 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 …
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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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
cuny.edu
http://faculty.baruch.cuny.edu/aapter/papers/innermodels.pdf
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INNER MODELS WITH LARGE CARDINAL FEATURES …
WEBIntroduction. The theme of this article is to investigate the extent to which several set-theoretic properties obtainable by forcing over universes with large cardinals must also …
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Mathematics Stack Exchange
https://math.stackexchange.com/questions/618780/...
What determines when an inner model is "canonical"?
WEBCanonical inner models $M$ are definable without parameters and, in fact, "locally" definable, that is, there is a formula $\psi_M$ such that $M=\{x\mid \psi_M(x)\}$. (Of …
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Canonical Model vs. Logical Model
SCVHistory.com
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N-Scale Model of Pioneer Oil Refinery - scvhistory.com
WEBN-scale model kit of the Pioneer Oil Refinery and Andrew's Station in Newhall, developed by San Francisco architect and master model railroader Thomas R. Knapp, AIA. …
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Santa Susana Pacific Model Railroad
WEBThe Santa Susana Pacific Model Railroad is an HO Scale Model Railroad Society based inside a class 22 Southern Pacific Railway Depot.
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Community Home Buying & Selling Real Estate Guide
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Silverthorne Archives - Community Home Buying & Selling Real …
WEBSilverthorne Tract – Simi Valley Floor Plans. Silverthorne Tract Models Simi Valley, California The Silverthorne Tract at Indian Hills Tract built in the late 1990s by Centex …
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Ventura County Museums
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Santa Susana Railroad Depot & Museum - Ventura County …
WEBSanta Susana Depot is a train station building located near the Santa Susana Pass in Simi Valley, California. Originally located on Los Angeles Avenue at Tapo Street, [1] the depot …
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