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Mar 26, 2012 at 23:31 comment added Carl Mummert @Lucas K.: "second-order arithmetic", and in particular $ACA_0$, is a first-order theory.
Mar 26, 2012 at 23:29 comment added Lucas K. Note that I was talking about second order logic, and not first order logic. A closure can be defined in second order logic. But I will read your answer more carefully tomorow.
Mar 26, 2012 at 23:06 history answered Andreas Blass CC BY-SA 3.0