Por Paulo Guilherme Santos (NOVA FCT and ISCAL).

We study the ω-reflexivity of theories T, i.e. the ability of a theory T to prove ω-con_{T_0}, with T_0 a finitely axiomatized sub-theory of T. We prove that, for every verifiably essentially reflexive theory T and every finitely axiomatized sub-theory T_0 of T, T+RFN_{\Sigma_2}(T) proves \ω-con_{T_0}. We develop a uniform version of ω-consistency, Uω-con_{T_0}, such that, for T and T_0 in the previous conditions, T proves Uω-con_{T_0}. n-consistency and theories of truth are also considered, namely Tr(PA) for which we get that Tr(PA) proves ω-con_{PA}.

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