Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Functional interpretation and modified realizability interpretation of the double-negation shift

Speaker: Philipp Gerhardy
Presentation: cie2006.pdf
Slot: Tue, 14:30-14:50, Faraday C (col. 3)

Abstract

In this paper, we investigate the relationship between the functional,
resp. the modified realizability, interpretation of finite and infinite
variants of the double-negation shift. The aim of these investigations
is to gain a better understanding of the existing (bar-recursive)
interpretations of the full, infinite
double-negation shift. In
particular, we obtain a new modified realizability interpretation of
the double-negation shift that is derived by extending the
corresponding interpretation of the intuitionistic principle 
  (NOT NOT P_0 & NOT NOT P_1) -> NOT NOT (P_0 & P_1) 
to the infinite case. 


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