|
|
|
|
LEADER |
01344nam a2200157Ia 4500 |
001 |
10.1017-jsl.2018.76 |
008 |
220511s2019 CNT 000 0 und d |
020 |
|
|
|a 00224812 (ISSN)
|
245 |
1 |
0 |
|a WEAKLY REMARKABLE CARDINALS, ERDAOS CARDINALS, and the GENERIC VOPĚNKA PRINCIPLE
|
260 |
|
0 |
|b Cambridge University Press
|c 2019
|
856 |
|
|
|z View Fulltext in Publisher
|u https://doi.org/10.1017/jsl.2018.76
|
520 |
3 |
|
|a We consider a weak version of Schindler's remarkable cardinals that may fail to be Σ2 - reflecting. We show that the Σ2-reflecting weakly remarkable cardinals are exactly the remarkable cardinals, and that the existence of a non-Σ2 -reflecting weakly remarkable cardinal has higher consistency strength: it is equiconsistent with the existence of an ω-Erdos cardinal. We give an application involving gVP, the generic Vopěnka principle defined by Bagaria, Gitman, and Schindler. Namely, we show that gVP + "Ord is not Δ2-Mahlo" and gVP(Π1) + "there is no proper class of remarkable cardinals" are both equiconsistent with the existence of a proper class of ω-Erdos cardinals, extending results of Bagaria, Gitman, Hamkins, and Schindler. Copyright © 2019 The Association for Symbolic Logic.
|
650 |
0 |
4 |
|a remarkable cardinals
|
650 |
0 |
4 |
|a virtual large cardinals
|
700 |
1 |
|
|a Wilson, T.M.
|e author
|
773 |
|
|
|t Journal of Symbolic Logic
|