Journal of Symbolic Logic 60 (2):640-653 (1995)
|Abstract||Let us define the intuitionistic part of a classical theory T as the intuitionistic theory whose proper axioms are identical with the proper axioms of T. For example, Heyting arithmetic HA is the intuitionistic part of classical Peano arithmetic PA. It's a well-known fact, proved by Heyting and Myhill, that ZF is identical with its intuitionistic part. In this paper, we mainly prove that TT, Russell's Simple Theory of Types, and NF, Quine's "New Foundations," are not equal to their intuitionistic part. So, an intuitionistic version of TT or NF seems more naturally definable than an intuitionistic version of ZF. In the first section, we present a simple technique to build Kripke models of the intuitionistic part of TT (with short examples showing bad properties of finite sets if they are defined in the usual classical way). In the remaining sections, we show how models of intuitionistic NF 2 and NF can be obtained from well-chosen classical ones. In these models, the excluded middle will not be satisfied for some non-stratified sentences|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Neil Tennant (1994). Intuitionistic Mathematics Does Not Needex Falso Quodlibet. Topoi 13 (2):127-133.
D. Dalen (1986). Glueing of Analysis Models in an Intuitionistic Setting. Studia Logica 45 (2):181 - 186.
Milan Božić & Kosta Došen (1984). Models for Normal Intuitionistic Modal Logics. Studia Logica 43 (3):217 - 245.
Victor N. Krivtsov (2000). A Negationless Interpretation of Intuitionistic Theories. I. Studia Logica 64 (3):323-344.
Michael Potter (1998). Classical Arithmetic as Part of Intuitionistic Arithmetic. Grazer Philosophische Studien 55:127-41.
Kosta Došen (1985). Models for Stronger Normal Intuitionistic Modal Logics. Studia Logica 44 (1):39 - 70.
Kai F. Wehmeier (1996). Classical and Intuitionistic Models of Arithmetic. Notre Dame Journal of Formal Logic 37 (3):452-461.
Daniel Dzierzgowski (1998). Finite Sets and Natural Numbers in Intuitionistic TT Without Extensionality. Studia Logica 61 (3):417-428.
Stefano Berardi (1999). Intuitionistic Completeness for First Order Classical Logic. Journal of Symbolic Logic 64 (1):304-312.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Recent downloads (6 months)0
How can I increase my downloads?