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\(\text{PA} (aa)\). (English) Zbl 0848.03018
\(\text{PA} (aa)\) is Peano Arithmetic formulated in stationary logic. It is not at all obvious that \(\text{PA} (aa)\) is consistent. The author shows that it is. He proves that the first-order consequences of \(\text{PA}(aa)+\) the scheme of determinateness for stationary logic are the same as those of the full second-order arithmetic CA. Two main results are: (1) Every model of \(\text{PA} (aa)\) is \(\omega_1\)-like; (2) Every countable model \((M,X)\) of CA can be elementarily extended to an \(\omega_1\)-like finitely determinate model of \(\text{PA} (aa)\).
MSC:
03C62 Models of arithmetic and set theory
03F35 Second- and higher-order arithmetic and fragments
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