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Reflection using the derivability conditions

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Matthews,  Seán
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Matthews, S., & Simpson, A. (1996). Reflection using the derivability conditions. In A. Ursini, & P. Agilanò (Eds.), Logic and Algebra (pp. 603-616). New York, USA: Marcel Dekker.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-AC02-0
Abstract
Reflection principles are a way to build non-conservative true extensions of a theory. However the application of a reflection principle needs a proof predicate, and the effort needed to provide this is so great as to be not really practical. We look at a possible way to avoid this effort by using, instead of a proof predicate, a predicate defined using only necessary `modal' properties. Surprisingly, we can produce powerful non-conservative extensions this way. But a reflection principle based on such a predicate is essentially weaker, and we also consider its limitations.