Hod dichotomy theorem
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). Nettet8. jul. 2024 · Woodin's HOD Dichotomy Theorem says that if an extendible cardinal exists, then either V and H O D are rather close or rather far apart. My question is …
Hod dichotomy theorem
Did you know?
Nettet1. jul. 2024 · This paper explores several topics related to Woodin's HOD conjecture. We improve the large cardinal hypothesis of Woodin's HOD dichotomy theorem from an … 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...
NettetThe HOD Dichotomy Theorem, which is not a difficult theorem to prove, establishes an unexpected and deep connection between V and definability. To illustrate, one curious corollary of the HOD Dichotomy Theorem is that if is an extendible cardinal then must … Nettet1. sep. 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 successors of singular cardinals greater ...
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 … Nettet(γ+)HOD = γ+. (2) Every regular cardinal greater than δ is measurable in HOD. In this note, we shall prove a dichotomy in which (2) is weakened to hold for all sufficiently large regular cardinals greater than δ; see Corollary 20. The full result can be found in [4] Theorem 212. Notice that we have stated the HOD dichotomy without deriving ...
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 rst few theorems of this …
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 … check car tollsNettetThe 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 … check cartoonNettetHugh Woodin: "The HOD dichotomy" Participants in this workshop. Lecture notes from this workshop by Hugh Woodin, Jacob Davis and Daniel Rodriguez (PDF) Workshop description A fundamental theorem in Set Theory is Jensen's Covering Lemma. This lemma is in essence a dichotomy theorem: either V is very close to L or V is very far … check car towing capacityNettetTheorem (HOD Dichotomy Theorem) Suppose that is an extendible cardinal. Then one of the following holds. (1) Every regular cardinal is !-strongly measurable in HOD. … check cartridge fuseNettetWoodin’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 … check cartridge ink level for hpNettetThe HOD dichotomy requires the existence of an extendible cardinal; a supercompact does not suffice. This kind of dichotomy (especially in light of the HOD conjecture) is fundamental for core models. 6 uncleu • 2 yr. ago Have you considered asking on MathOverflow? 2 [deleted] • 2 yr. ago [removed] More posts you may like … flashcards the method 2NettetDefine 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 … check cartridge ink