7 problems

Let $C_2(0)=0$ and $C_2(n+1)=C_2(n)+2^{C_2(n)}$, and define $f(n)=2^{2^{C_2(n)}}$. For an elementary embedding $j$, write $\jsub{m}$ for its $m$-fold iterate and let $\gamma_k$ den…

For each $n$, let $a,b<2^{n-1}$ satisfy $p_n(a)=p_n(b)=2^k$. Let $c$ be the least element such that $\gamma_k$ is in the range of $c$, and let $c\gamma_i=\gamma_k$. Assume that…

For each $n$, let $A_n$ be the cyclic algebra considered in the paper. If $a<2^n-1$, write $p_n(a)=2^k$, and if $c+1$ is the threshold of $a$ in $A_n$, require that…

Let $\Gamma$ be the set of critical points of the embeddings in $\Cal A$, and let $\Sigma$ be the closure of $\Gamma$ under $a"\alpha=\sup\{a\xi:\xi<\alpha\}$ for $a\in\Cal A$. Let…

The Extender Embedding Axiom (EEA) is the assertion concerning elementary embeddings associated with the relationship between superstrong and tall cardinals described in the surrou…

The question concerns elementary embeddings of the universe into a fixed model of set theory. In ZFC, distinct normal ultrafilters can consistently have the same ultrapower, while…

Infinite-family conjecture. If $T$ does not have the Schröder–Bernstein property, then there is an infinite collection of models of $T$ that are pairwise nonisomorphic and pairwise…