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\(V = L\) and intuitive plausibility in set theory. A case study. (English) Zbl 1258.03070

Summary: What counts as an intuitively plausible set-theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen’s positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of set-theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics.

MSC:

03E45 Inner models, including constructibility, ordinal definability, and core models
00A30 Philosophy of mathematics
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