Abstract
We prove two conservation results involving a generalization of the principle of strict \({\Pi^1_1}\)-reflection, in the context of bounded arithmetic. In this context a separation between the concepts of bounded set and binary sequence seems to emerge as fundamental.
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This work was partially supported by FCT, CMAF—Universidade de Lisboa, Financiamento Base 2008 ISFL/1/209.
The author is also thankful to an anonymous referee for his valuable remarks contributing for making the final version of the present paper more readable and by correcting an historical inaccuracy concerning the origins of the strict \({\Pi^1_1}\) -reflection principle.
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Fernandes, A.M. Strict \({\Pi^1_1}\)-reflection in bounded arithmetic. Arch. Math. Logic 49, 17–34 (2010). https://doi.org/10.1007/s00153-009-0157-z
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DOI: https://doi.org/10.1007/s00153-009-0157-z