Chan, W. (2026). The ABCD hypothesis. Proceedings of the National Academy of Sciences of the United States of America, 123(44), Article e2621223123. https://doi.org/10.1073/pnas.2621223123
Proceedings of the National Academy of Sciences of the United States of America
-
ISSN:
0027-8424
-
Date (published):
3-Nov-2026
-
Number of Pages:
6
-
Publisher:
National Academy of Sciences
-
Peer reviewed:
Yes
-
Keywords:
Cardinality; Cardinal Exponentiation; Determinacy
en
Abstract:
If α and β are cardinals, then the cardinal exponentiation αβ is the set of all functions from α into β. The ABCD hypothesis is the statement that for all infinite cardinals α≤β and γ≤δ, |αβ|≤|γδ| if and only if α≤γ and β≤δ. The Axiom of Determinacy, AD, states that every two-player infinite game on ω has a winning strategy for one of the two players. Let Θ be the supremum of the ordinals onto which R surjects. This paper will show that if AD holds and V=L(R), then the ABCD hypothesis holds below Θ.
en
Project title:
Determiniertheit und Woodin Limes von Woodin Kardinalzahlen: Y1498 (FWF - Österr. Wissenschaftsfonds) Klassifikation abgeleiteter Modelle der Determiniertheit: I6087-N (FWF - Österr. Wissenschaftsfonds) Mathematische Strukturen in dem regulären Universum: PAT1651926 (FWF - Österr. Wissenschaftsfonds)
