Conservativity of SPOT+ plus Countable Standardization (SC) over ZF

Determine whether the nonstandard set theory SPOT+ together with the axiom schema SC (Countable Standardization) is a conservative extension of ZF.

Background

SPOT is designed as a conservative extension of ZF by weakening Standardization while retaining key nonstandard tools such as Transfer and Standard Part. SPOT+ further augments SPOT with SN (Standardization for parameter-free st-E-formulas) and SF (Standardization over standard finite sets).

The schema SC (Countable Standardization) strengthens available standardization. Whether combining SPOT+ with SC remains conservative over ZF is explicitly stated as open, marking a boundary case for how far standardization can be extended without increasing proof-theoretic strength beyond ZF.