Prolegomenon to any future neo-logicist set theory: Abstraction and indefinite extensibility

The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? 2 Framework 3 GOOD candidates, indefinite extensibility 4 The framework of (RV) alone, or almost alone 5 The axioms 6 Brief closing.
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DOI 10.1093/bjps/54.1.59
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J. P. Studd (forthcoming). Abstraction Reconceived. British Journal for the Philosophy of Science:axu035.
Jonathan Payne (2013). Abstraction Relations Need Not Be Reflexive. Thought: A Journal of Philosophy 2 (2):137-147.

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