Rosser orderings and free variables

Studia Logica 50 (1):71 - 80 (1991)

Authors
Dick De De Jongh
University of Amsterdam
Abstract
It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R –. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts oneself to usual proof predicates.
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DOI 10.1007/BF00370388
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Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.

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A Small Reflection Principle for Bounded Arithmetic.Rineke Verbrugge & Albert Visser - 1994 - Journal of Symbolic Logic 59 (3):785-812.
Efficient Metamathematics. Rineke - 1993 - Dissertation, Universiteit van Amsterdam

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