LD-algebras beyond I0

TL;DR

This paper introduces a new algebraic operation for embeddings at levels above I0, revealing that the resulting LD-algebras can differ significantly from those at I3, expanding understanding of high-level set-theoretic embeddings.

Contribution

It defines an operation for embeddings at I0 and higher, and proves these generate LD-algebras that differ from the well-studied I3 case.

Findings

Generated LD-algebras differ from I3 algebra

Introduced a new operation for embeddings above I0

Established algebraic properties of these new structures

Abstract

The algebra of embeddings at the I3 level has been deeply analyzed, but nothing is known algebra-wise for embeddings above I3. In this paper it is introduced an operation for embeddings at the level of I0 and above, and it is proven that they generate an LD-algebra that can be quite different from the I3 one.