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Results tagged with large-cardinals
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user 113405
8
votes
Accepted
Large cardinal near inconsistencies
I would argue that a "restricting versions" of large cardinals are such.
Starting from the top down, we have the inconsistent Berkeley cardinals:
$κ$ is Berkeley if for every transitive $M\ni\kappa$ …
- 1,676
3
votes
Accepted
Can we iteratively reflect on self elementary embeddable stages of the cumulative hierarchy?
$\newcommand\Ord{\mathit{Ord}}$The edit to the question has changed it enough so I think it deserves its own answer.
I assume that in reflection we have $\forall \vec{x} \in W_\alpha \, (\phi \to \ph …
- 1,676
6
votes
Can we iteratively reflect on self elementary embeddable stages of the cumulative hierarchy?
Any model of $ZF$+stationary proper class of $I3$ ordinals (whose consistency strength is at most $ZF$+$I2$) where $W_α$ is listing of $V_{κ}$ where $κ$ is $I3$ and $j_α$ the witness of $I3(V_κ)$ will …
- 1,676