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Let $\lambda$ be a cardinal. Let $\mathcal{E}_{\lambda}$ be the set of all elementary embeddings from $V_{\lambda}$ to $V_{\lambda}$. If $f:V_{\lambda}\rightarrow V_{\lambda}$ is a function and $\gamm …

Let $\kappa$ be a strong cardinal. Then for each $\lambda\geq\kappa$ does there exist a $\mu>\lambda$ such that if $U$ is a $\kappa$-complete ultrafilter on $\lambda$ and $j:V\rightarrow M,V_{\mu}\sub …

Does there exist a set $I$ and an ultrafilter $U$ on $I$ and a non-trivial elementary embedding $j:V^{I}/U\rightarrow V^{I}/U$? So the Kunen inconsistency result states that there does not exist a no …

Suppose that $\kappa$ is a cardinal, $X$ is a set with $|X|>\kappa$, and $\mathcal{U}\subseteq P(P_{\kappa}(X))$ is a normal ultrafilter. We say that a collection $C\subseteq P_{\kappa}(X)$ is a condi …

In this question, I asked about how slowly the Fibonacci terms in a algebra of elementary embeddings could grow, but I did not inquire if there was a limit to how quickly the Fibonacci terms could gro …

Can there exist non-trivial elementary embeddings $j,k:V_{\lambda+1}\rightarrow V_{\lambda+1}$ along with a strictly increasing function $r:\omega\rightarrow\omega$ such that $j^{r(2n)}(\mathrm{crit}( …

If $\lambda$ is a cardinal, then let $\mathcal{E}_{\lambda}$ be the set of all elementary embeddings from $V_{\lambda}$ to $V_{\lambda}$. If $j,k\in\mathcal{E}_{\lambda}$, then define $j*k=\bigcup_{\a …

Let $j,k:V_{\lambda}\rightarrow V_{\lambda}$ be inequivalent elementary embeddings. Then let $\theta(j,k)$ be the largest limit ordinal $\gamma$ such that $j(x)\cap V_{\gamma}=k(x)\cap V_{\gamma}$ for …

Let $B_{\infty}$ denote the infinite strand braid group. Let $\text{sh}:B_{\infty}\rightarrow B_{\infty}$ be the homomorphism defined by $\text{sh}(\sigma_{i})=\sigma_{i+1}$ whenever $i\geq 1$. Give …

If $j$ is a function with $V_{\lambda+1}\subseteq\mathrm{Dom}(f)$, then define a mapping $j\upharpoonright_{\lambda+1}:V_{\lambda+1}\rightarrow V_{\lambda+1}$ by letting $j\upharpoonright_{\lambda+1}( …

Suppose that $\lambda$ is a cardinal. Let $\mathcal{E}_{\lambda}$ be the set of all elementary embeddings from $V_{\lambda}$ to $V_{\lambda}$. If $j,k\in\mathcal{E}_{\lambda}$, then define $j[k]=\bigc …

I want to know if there are fairly simple combinatorial necessary conditions for when a direct limit of ultrapowers of $V$ is well-founded similar to $\sigma$-completeness. By combinatorial, I mean th …

Let's call a cardinal $\delta$ an $\text{I1}$-tower cardinal if for each $A\subseteq V_{\delta}$, there exists a $\kappa<\delta$ such that whenever $\kappa<\alpha<\delta$ there is some $\lambda<\delta …

Suppose that $(X,*,1)$ satisfies the following identities: $x*(y*z)=(x*y)*(x*z),1*x=x,x*1=1$. Define the Fibonacci terms $t_{n}(x,y)$ for $n\geq 1$ by letting $$t_{1}(x,y)=y,t_{2}(x,y)=x,t_{n+2}(x,y) …

For this question, suppose that there exists a rank-into-rank cardinal. Let $\mathcal{E}_{\lambda}$ be the set of all elementary embeddings $j:V_{\lambda}\rightarrow V_{\lambda}$. Give $\mathcal{E}_{\ …