The strength of replacement in weak arithmetic
<|reference_start|>The strength of replacement in weak arithmetic: The replacement (or collection or choice) axiom scheme asserts bounded quantifier exchange. We prove the independence of this scheme from various weak theories of arithmetic, sometimes under a complexity assumption.<|reference_end|>
@article{cook2004the,
    title={The strength of replacement in weak arithmetic},
    author={Stephen Cook and Neil Thapen},
    journal={arXiv preprint arXiv:cs/0409015},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0409015},
    primaryClass={cs.LO cs.CC}
}