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6:17 AM
Two new tags and . They were both created in the same question - which does not have a top-level tag: Is diamond consistent with 2nd order PA?
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Q: Is diamond consistent with 2nd order PA?

Vladimir KanoveiIf $T$ is a theorem of ZF which says something only about reals, then one may want to prove $T$ using a theory like 2nd order PA or related theories like ZFC$^-$ or GBC$^-$ (minus accounts for the absence of the Power Set axiom). In many cases this goes through, sometimes rather straightforwardly...

In mathematics, and particularly in axiomatic set theory, the diamond principle ◊ is a combinatorial principle introduced by Ronald Jensen in Jensen (1972) that holds in the constructible universe (L) and that implies the continuum hypothesis. Jensen extracted the diamond principle from his proof that the axiom of constructibility (V = L) implies the existence of a Suslin tree. == Definitions == The diamond principle ◊ says that there exists a ◊-sequence, a family of sets Aα ⊆ α for α < ω1 such that for any subset A of ω1 the set of α with A ∩ α = Aα is stationary in ω1. There are severa...
To me, the tag seems like a reasonable tag for that question: Is diamond consistent with 2nd order PA? (Of course, the question whether or not the two tags created there should be kept is a separate question.)
 
6:47 AM
And perhaps might be reasonable, too?
 

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