The Unintended Interpretations of Intuitionistic Logic
Wim Ruitenburg · Birkhäuser Boston eBooks · 2008
We present an overview of the unintended interpretations of intuitionistic logic that arose after Heyting formalized the “observed regularities” in the use of formal parts of language, in particular, first-order logic and Heyting Arithmetic. We include unintended interpretations of some mild variations on “official” intuitionism, such as intuitionistic type theories with full comprehension and higher order logic without choice principles or not satisfying the right choice sequence properties. We conclude with remarks on the quest for a correct interpretation of intuitionistic logic. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.