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- Descriptive inner model theory is an area of set theory that uses tools from inner model theory and descriptive set theory to study the internal structure of models of determinacy and to build models of determinacy from various large cardinals. It aims to create links between foundational frameworks1. Inner model theory studies the relationships of these models to determinacy, large cardinals, and descriptive set theory2. The main technical goal of descriptive inner model theory is to construct canonical models of fragments of set theory, known as mice, that capture the truth holding in the universe3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Descriptive inner model theory is an area of set theory that uses tools from inner model theory and descriptive set theory to study the internal structure of models of determinacy and also to develop tools to build models of determinacy from various large cardinals. One of its main goals is to create links between various foundational frameworks.export.arxiv.org/pdf/2307.00109Ordinarily 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.en.wikipedia.org/wiki/Inner_model_theoryDescriptive 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 fragments of set theory, namely mice, that capture the truth holding in the universe.arxiv.org/pdf/1206.2712.pdf
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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 fragments of set theory, namely mice, that capture the truth holding in the universe. An …
See results only from arxiv.orgTranslation procedures in de…
[Submitted on 12 Oct 2021] Translation procedures in descriptive inner model …
[1206.2712] Descriptive inne…
Descriptive inner model theory. Grigor Sargsyan. A paper for general audience …
arXiv:2307.00109v1 [math.L…
Descriptive inner model theory is an area of set theory that uses tools from inner …
WebarXiv. Authors: Grigor Sargsyan. Rutgers, The State University of New Jersey. Citations (28) References (66) Abstract. The purpose of this paper is to outline some recent progress in descriptive...
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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WebAbstract. The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas.
WebOur outline of basic inner model theory occupies sections two through six of this paper. In sections seven and eight we present an application of this theory in descriptive set theory: we show that the model HODL(R) of all sets hereditarily ordinal definable in L(R) is (essentially) an extender 5
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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 form of the canonical inner models up through models with supercompacts. The models are (or will be) of the form L[EE], where EE is a coherent sequence of extenders.
WebDescriptive inner model theory. organized by Ralf Schindler and John Steel. Workshop Summary. The main goal of the workshop was to present and discuss recent advances concerning the core model induction technique, the analysis of the hereditarily ordinal de nable sets in models of AD, and inner models with long extenders.
WebJun 13, 2012 · Descriptive inner model theory. Grigor Sargsyan. A paper for general audience about descriptive inner model theory. Comments: To appear in BSL. Subjects: Logic (math.LO) Cite as:
WebDESCRIPTIVE INNER MODEL THEORY GRIGOR SARGSYAN Dedicated to my father Edvard Sargsyan on the occasion of his 60 th birthday Abstract. The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from ...
WebDescriptive inner model theory is the study of connections between descript-ive set theory and inner model theory. Such connections form the basis of the core model induction, which we use to prove relative consistency results relating strong forms of the Axiom of Determinacy with the existence of a strong ideal on }! 1
WebUBH for nice trees is crucial in constructing canonical inner models of large cardinals (e.g. of superstrong, supercompact, and beyond), the main objective of inner model theory. Determining whether UBH holds for nice trees is, therefore, a fundamental problem in …
[PDF] Descriptive inner model theory | Semantic Scholar
WebAbstract The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas.
WebDescriptive inner model theory is an area of set theory that uses tools from inner model theory and descriptive set theory to study the internal structure of models of determinacy and also to develop tools to build models of determinacy from various large cardinals.
An exceptional review about inner model theory
WebAug 27, 2016 · There has been a great deal of progress on this question using methods from inner model theory. The goal of the last two sections of the Outline is to introduce two important topics of descriptive inner model theory. The first one is mouse capturing.
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 (partially) answering these questions roughly from the early 2000's to present. Most of the major questions are still open.
Grigor Sargsyan, Descriptive inner model theory - PhilPapers
WebAbstract. The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas.
Set Theory: Exploring Independence and Truth | SpringerLink
WebOverview. Authors: Ralf Schindler. Provides a fairly self-contained introduction to set theory, in particular to the theory of inner models and forcing. Presents essential aspects of set theory which are required in understanding modern developments of …
WebThe purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects ...
Translation procedures in descriptive inner model theory
Web[Submitted on 12 Oct 2021] Translation procedures in descriptive inner model theory. Grigor Sargsyan. We develop a basic translation procedure that translates a hod mouse to an equivalent mouse. Unlike the translation procedure used by Steel and Zhu, our procedure works in a coarse setting without assuming AD.
Descriptive inner model theory | American Inst. of Mathematics
WebThis workshop, sponsored by AIM and the NSF, will be devoted to inner model theory and descriptive set theory. The main topics for the workshop are the core model induction technique, the analysis of the hereditarily ordinal definable sets in models of $AD$, and inner models with long extenders.
NSF Award Search: Award # 1954149 - Descriptive Inner Model …
WebDescriptive Inner Model Theory is one part of what is now called Godel's Program, which is the program of removing undecidability from mathematics by studying stronger and stronger natural axiomatic systems extending ZFC that decide more and more natural questions about sets of reals and other mathematical objects.
Descriptive Inner Model Theory and Its Applications
WebDescriptive Inner Model Theory and Its Applications. ABSTRACT. The Zermelo-Fraenkel axioms plus the Axiom of Choice (ZFC) have been widely accepted as a foundation for mathematics; virtually all branches of mathematics that have been studied and applied to other scientific fields can be interpreted in ZFC.
1st IRVINE
WebAug 6, 2010 · 1st IRVINE CONFERENCE on DESCRIPTIVE INNER MODEL THEORY and HOD MICE Department of Mathematics, UC Irvine July 18 -- 29, 2016. Supported by: NSF Grants DMS-x, DMS-1044150, DMS-y, and UCI CORCL . Organizers: Grigor Sargsyan (Rutgers), John Steel (Berkeley), Nam Trang (Irvine), Martin Zeman (Irvine)
Berkeley conference on inner model theory, the core model …
WebAbstract: The Ultrapower Axiom (UA) is a combinatorial principle motivated by inner model theory which provides an elegant setting for developing the part of large cardinal theory that concerns countably complete ultrafilters.
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