Hod dichotomy theorem

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August undefined, 2024

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). Nettetlarge cardinal techniques and results developed from Woodin’s work on the HOD-Dichotomy to determine the structural resemblance of HOD to V . Whereas standard …

GabrielGoldberg arXiv:2102.05463v4 [math.LO] 18 Feb 2024

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... 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 … mechanical speed variator principle

Hugh Woodin at Cornell University on April 7, 2012 - CMU

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 … Nettetin V derives a sharp dichotomy between HOD being close/far from V, as shown by Woodin’s HOD-Dichotomy theorem ([12]). Theorem 1.4 (HOD Dichotomy, [14]). If δis an extendible cardinal then one of the following holds. (1) Every cardinal ηabove δwhich is singular in V, is singular in HOD and (η+)HOD = η+. 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 ... mechanical speedometer

§1. Introduction. The Inner Model Program began with Gödel

In Search of Ultimate-L the 19th Midrasha Mathematicae Lectures

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 … 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 peloton free trialNettet(1) For every singular cardinal γ > δ, γ is singular in HOD and (γ+)HOD = γ+. (2) Every regular cardinal greater than δ is measurable in HOD. In this note, we shall prove a … mechanical speed variator

"NettetThe HOD dichotomy HOD under determinacy Embeddings of HOD The optimal hypothesis for the HOD dichotomy Theorem Suppose is strongly compact. Then one … " - Hod dichotomy theorem

Hod dichotomy theorem

[2107.00513] Strongly compact cardinals and ordinal definability

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 … 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 …

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NettetarXiv:1911.04568v2 [math.LO] 31 Dec 2024 ON ω-STRONGLY MEASURABLE CARDINALS OMER BEN-NERIA AND YAIR HAYUT Abstract. We prove several consistency results concerning the notion of 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 …

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 ... 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 …

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 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 …

NettetA version of Woodin's HOD dichotomy is proved assuming the existence of just one strongly compact cardinal. Discover the world's research Available via license: CC BY …

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). peloton free shirt 100 ridesNettetThe 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). peloton free trial ukNettet20. 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 … mechanical spice downloadNettetWe 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 … peloton free subscriptionNettetThe 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. mechanical speedometer converterNettetThe 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). mechanical speedometer calibrationNettetWoodin’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 … mechanical speedometer repair