Topic
Inner model
About: Inner model is a research topic. Over the lifetime, 111 publications have been published within this topic receiving 1422 citations.
Papers published on a yearly basis
Papers
1 Jan 2010
TL;DR: In this paper, the basic theory of canonical inner models satisfying large cardinal hypotheses is presented, along with a proof that the hereditarily ordinal definable sets of L(ℝ) constitute a canonical inner model.
Abstract: 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 structural analysis modulo iterability assumptions. It then outlines how to construct canonical inner models, and prove their iterability, in roughly the greatest generality in which it is currently known how to do this. The paper concludes with some applications: genericity iterations, proofs of generic absoluteness, and a proof that the hereditarily ordinal definable sets of L(ℝ) constitute a canonical inner model.
210 citations
1 Mar 1984
TL;DR: The model K() as mentioned in this paper is a new inner model of ZFC which can contain measurable cardinals of high order and has many of the basic properties of L: the GCH and ⃟ hold and there is a definable well ordering which is on the reals.
Abstract: The model K() presented in this paper is a new inner model of ZFC which can contain measurable cardinals of high order. Like the model L() of [14], from which it is derived, K() is constructed from a sequence of filters such that K() satisfies for each (α, β) e domain () that (α,β) is a measure of order β on α and the only measures in K() are the measures (α,β). Furthermore K(), like L(), has many of the basic properties of L: the GCH and ⃟ hold and there is a definable well ordering which is on the reals. The model K() is derived from L() by using techniques of Dodd and Jensen [2–5] to build in absoluteness for measurability and related properties.
137 citations
TL;DR: It is shown that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Godel's constructible universe L.
Abstract: We investigate both iteration hypotheses and extender models at the level of one supercompact cardinal. The HOD Conjecture is introduced and shown to be a key conjecture both for the Inner Model Program and for understanding the limits of the large cardinal hierarchy. We show that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Godel's constructible universe L. Whether or not this "ultimate" L exists is now arguably the central issue for the Inner Model Program.
91 citations
TL;DR: It is shown that the reals in the minimal iterable inner model having n Woodin cardinals are precisely those which are Δ n + 2 1 definable from some countable ordinal.
70 citations
TL;DR: In this article, the authors show that the generic mantle of V is the intersection of all HODs of all set-forcing extensions of V and the generic HOD is always a model of ZFC.
70 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 7 |
| 2020 | 12 |
| 2019 | 3 |
| 2018 | 4 |
| 2017 | 5 |
| 2016 | 4 |