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We present four different approaches to prove the soundness theorem for variants with t-truth of functional interpretations. To showcase our different methods we focus on the intuitionistic nonstandard bounded functional interpretation of the nonstandard extensional Heyting arithmetic in all finite types because a version with t-truth for this interpretation has not been given before. Also, because it is a more involved interpretation than others since it includes both nonstandard principles and majorisability. This leads us to believe that if the approaches work for this more complicated functional interpretation, then they should also work for simpler functional interpretations (and realisabilities). [ABSTRACT FROM AUTHOR]

This article systematically investigates so-called 'truth variants' of several functional interpretations. We start by showing a close relation between two variants of modified realizability, namely modified realizability with truth and q-modified realizability. Both variants are shown tobe derived from a single 'functional interpretation with truth' of intuitionistic linear logic. This analysis suggests that several functional interpretations have truth and q-variants. These variants, however, require a more involved modification than the ones previously considered. Following this lead we present truth and q-variants of the Diller-Nahm interpretation, the bounded modified realizability and the bounded functional interpretation (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The article presents a mathematical solution to the problem of determining a triangle using modulo similarity.