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Results tagged with embeddings
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user 160347
7
votes
Accepted
Can there exist such a sequence of elementary embeddings of the universe to itself?
It was pointed out by Monroe that if $\lambda$ is a limit and $j:V_\lambda\to V_\lambda$ is elementary and $j_n$ is the $n$th iterate, i.e. $j_0=j$ and $j_{n+1}=j_n(j_n)$, and $\kappa_n=\mathrm{crit}( …
- 9,902
4
votes
Accepted
Is this sequence of embeddings possible?
Work in ZF+AC$_\omega$. Suppose $V_\theta$ is inaccessible. Suppose $j,k:V_{\theta+1}\to V_{\theta+1}$ are elementary and $\mathrm{crit}(j)=\mathrm{crit}(k)=\kappa$ and $\kappa_\omega(j)<k(\kappa)$. H …
- 9,902
10
votes
Accepted
Can we have mutual elementary embeddability between distinct transitive sets?
There are examples of this where $M,N$ are also models of ZFC, in the following paper, which is joint with Monroe Eskew, Sy Friedman and Yair Hayut: https://arxiv.org/abs/2108.12355
Thus, you certainl …
- 9,902