On the utility of Robinson-Amitsur ultrafilters. II

TL;DR

This paper extends the embedding results of ideal-determined algebraic systems into ultraproducts to more general systems and ultrafilters, clarifies the scope, and corrects a previous mistake regarding homomorphisms.

Contribution

It generalizes previous embedding results to arbitrary algebraic systems and ultraproducts over κ-complete ultrafilters, and addresses a correction in the theory.

Findings

Extended embedding results to arbitrary algebraic systems.

Analyzed the applicability scope of ultraproduct embeddings.

Corrected a mistake related to homomorphisms from ultraproducts.

Abstract

We extend the result of arXiv:0911.5414 about embedding of ideal-determined algebraic systems into ultraproducts, to arbitrary algebraic systems, and to ultraproducts over $\kappa$-complete ultrafilters. We also discuss the scope of applicability of this result, and correct a mistake from the previous paper concerning homomorphisms from ultraproducts.