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Mar 11 at 14:50 comment added user21820 This does not support ZFC with Replacement. Boolos said so explicitly himself; he said that Replacement is "not derived from the iterative conception". Moreover, almost all modern mathematics can be done within B[ounded]ZFC (i.e. with both Specification and Replacement restricted to Δ0 defining formulae), and this is at least reasonably cogent and in line with the iterative conception, in contrast to the unjustified unbounded schemas. We can conceivably extend to BZFC^P, where "^P" means that powerset is an inbuilt function-symbol, and BZFC^P suffices for essentially all ordinary mathematics.
Jun 19, 2010 at 5:03 vote accept Ewan Delanoy
Jun 18, 2010 at 20:15 history answered Dan Piponi CC BY-SA 2.5