We investigate the structure of rank-to-rank elementary embeddings at successor rank, working in $\mathrm{ZF}$ set theory without Axiom Choice. Recall that set-theoretic universe is naturally stratified by cumulative hierarchy, whose levels $V\_\alpha$ are defined via iterated application power operation, starting from $V\_0=\emptyset$, setting $V\_{\alpha+1}=\mathcal{P}(V\_\alpha)$, and taking...

Abstract Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding this mechanism, we approach technology as body knowledge consisting interlinked inventions. can then be understood extent to which inventions build on other within that same knowledge. The therefore ...