Errata: multi-level nonstandard analysis and the axiom of choice

The formulation of Proposition 3.3 (Factoring Lemma) on page 10 of the following paper is incorrect:Multi-level nonstandard analysis and the axiom of choice, J. Logic & Analysis 16 (2024) 1-29 Consequently, the notion of admissible formula (Definition 4.1 on page 11) has to be weakened.While the new formulations suffice for the proofs in Sections 5 and 6, Proposition 4.5 on page 13 cannot be proved in SCOTS and Section 7, which depends on this proposition in an essential way, is unjustified.