A multiverse perspective on the axiom of constructibility
I shall argue that the commonly held V ≠= L via maximize position, which rejects the axiom of constructibility V = L on the basis that it is restrictive, implicitly takes a stand in the pluralist debate in the philosophy of set theory by presuming an absolute background concept of ordinal. The argum...
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| Format: | Book section |
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World Scientific Publishing
2014
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| Summary: | I shall argue that the commonly held V ≠= L via maximize position, which rejects the axiom of constructibility V = L on the basis that it is restrictive, implicitly takes a stand in the pluralist debate in the philosophy of set theory by presuming an absolute background concept of ordinal. The argument appears to lose its force, in contrast, on an upwardly extensible concept of set, in light of the various facts showing that models of set theory generally have extensions to models of V = L inside larger set-Theoretic universes. |
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