Hod dichotomy theorem

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August undefined, 2024

NettetTheorem. 对于所有的 b\in \mathbb{R} 有 \zeta(1+bi) \neq 0. 重要的：这个结果给了质数定理证明的关键部分，通过扩展 \zeta(s) 的 zero-free 区域来包含 line \Re(s)=1. 这似乎很 … NettetThe HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V (in the sense that it correctly computes successors of singular cardinals greater than δ) or HOD is “far” from V (in the sense that all regular cardinals greater than or equal to δ are measurable in HOD).

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NettetHence Berkeley cardinals and HOD-Berkeley cardinals are, in a sense, the HOD-analogues for 0]. The following main theorems of [1] capture this motto. Main Theorem 1 (LCBC Corollary 8.1). If the Weak HOD Conjecture is true, then the former side of Theorem2holds where HOD is \close" to V and Berkeley Cardinals are inconsistent with … NettetWe prove that the HOD hypothesis holds if and only if every regular cardinal above the first strongly compact cardinal carries an ordinal definable omega-Jonsson algebra. We … dementia friends training courses

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NettetDefine hod. hod synonyms, hod pronunciation, hod translation, English dictionary definition of hod. n. 1. A trough carried over the shoulder for transporting loads, as of … NettetAn introduction to large cardinals and their inner models, with special emphasis on Woodin's recent advances toward finding an ultimate version of Godel's L. Topics … Nettet30. nov. 2024 · cardinal hierarchy and the HOD Dichotomy Theorem are thethree main motivations for the HOD Hypothesis. (1) Inner model theory has a long and complex history, starting with Jensen’s work on... dementia friendly wnc

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Nettetin set theory, such as Woodin’s HOD-Dichotomy theorem, the proof by Aspero-Schindler that MM++ implies the (*) axiom, and some theorems, due to several authors, that provide new in-sights into the hierarchy of large cardinals, including large cardinals that contradict the Axiom of Choice. 3 NettetHydrogen on Demand. HOD. Halo Occupation Distribution (astronomy) HOD. Hypertrophic Osteodystrophy. HOD. Hydrogen-Oxygen-Deuterium. showing only Science & … dementia friends e learningNettet1. jul. 2024 · We show that the HOD hypothesis is equivalent to a uniqueness property of elementary embeddings of levels of the cumulative hierarchy. We prove that the HOD … few u.s. doctors are specially trained in

"NettetTheorem (HOD Dichotomy Theorem) Suppose that is an extendible cardinal. Then one of the following holds. (1) Every regular cardinal is !-strongly measurable in HOD. … " - Hod dichotomy theorem

Hod dichotomy theorem

The HOD Dichotomy (Chapter 13) - Appalachian Set Theory

NettetThe HOD dichotomy HOD under determinacy Embeddings of HOD Woodin’s HOD dichotomy Theorem (Woodin) Assume is extendible. Then exactly one of the following holds: (1) For any set S HOD, there is a set T 2HOD of cardinality max(jSj; ) such that S T. (2) Every regular cardinal is measurable in HOD. Looks just like the situation with L. NettetThe HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy.

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NettetWoodin’s HOD conjecture states that conclusion (1), which in this context is known as the HOD hypothesis,1 is provable from large cardinal axioms. The ﬁrst few theorems of … Nettet(1)Foreverysingularcardinal>κ, +issingularinHODand( )HOD= +. (2)Every regular cardinal κis a measurable cardinal inHOD. IntheﬁrstalternativeHODis“close”toV,andinthesecondalternative, HODis“far”fromV. There is an important foundational diﬀerence between the two …

NettetThe HOD dichotomy HOD under determinacy Embeddings of HOD The optimal hypothesis for the HOD dichotomy Theorem Suppose is strongly compact. Then one … NettetAn introduction to large cardinals and their inner models, with special emphasis on Woodin's recent advances toward finding an ultimate version of Godel's L. Topics include: Weak extender models, the HOD Dichotomy Theorem, and the HOD Conjecture. Prerequisites: Prerequisite: Mathematics 145A Department: Mathematics Cross …

Nettet5. des. 2012 · The HOD Dichotomy (Chapter 13) - Appalachian Set Theory Home > Books > Appalachian Set Theory > The HOD Dichotomy 13 - The HOD Dichotomy … NettetThe HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V (in the sense that it correctly computes successors of singular cardinals greater than δ) or HOD is “far” from V (in the sense that all regular cardinals greater than or equal to δ are measurable in HOD). The question is whether the future …

Nettet20. aug. 2024 · The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ , then either HOD is “close” to V (in the sense that it correctly computes …

NettetWoodin’s HOD dichotomy Theorem (Woodin) Assume is extendible. Then exactly one of the following holds: (1) For all , HOD has the -cover property. (2) Every regular cardinal is inaccessible in HOD. Looks just like the situation with L. Except no large cardinal axiom few và fewerNettetUsing these theorems, we prove the dichotomy involving successors of singulars. Proof of Theorem 1.1. By Lemma 2.3 (and Theorem 2.1), we can assume that HOD has the κ-cover property. Fix a singular strong limit cardinal λ > κ. Theorem 1.2 easily implies that λ is singular in HOD. Let γ = λ+HOD. Since γ is regular in HOD, Theorem 1.2 implies dementia friends of indianaNettetThe Second Clue: HOD Dichotomy Theorem ... I The evidence suggests that the theorem is not a dichotomy theorem at all: I HOD should just be close to V. Re ection A sentence ’is a 2-sentence if it is of the form: I There exists an ordinal such that V j= ; for some sentence . In the context of ZFC: I CH is expressible by a 2-sentence. fewvf