Hod dichotomy theorem
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 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 …
Hod dichotomy theorem
Did you know?
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 ... 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+.
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 …
NettetHodology is the study of pathways. The word derives from the Greek hodos, meaning "path".It is used in various contexts: In neuroscience, it is the study of the … 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 …
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 …
NettetThe HOD Dichotomy Theorem generalizes this to HOD, showing that if there is an extendible cardinal then V must be either very close to HOD or very far from HOD. The … tax maryboroughNettetHydrogen on Demand. HOD. Halo Occupation Distribution (astronomy) HOD. Hypertrophic Osteodystrophy. HOD. Hydrogen-Oxygen-Deuterium. showing only Science & … tax marriage allowance transferNettetThe 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. tax married filing jointly 2022NettetWe 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 … the cleveland popcorn companytax marital status optionsNettetHugh 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 … tax marriage allowances 2022/2023NettetThe 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. tax masonoh.org