Forcing and reducibilities. II. forcing in fragments of analysis

Journal of Symbolic Logic 48 (3):724-743 (1983)
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Partially definable forcing and bounded arithmetic.Albert Atserias & Moritz Müller - 2015 - Archive for Mathematical Logic 54 (1):1-33.

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Some applications of forcing to hierarchy problems in arithmetic.Peter G. Hinman - 1969 - Mathematical Logic Quarterly 15 (20-22):341-352.

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