Models of intuitionistic TT and N

Journal of Symbolic Logic 60 (2):640-653 (1995)
  Copy   BIBTEX


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



    Upload a copy of this work     Papers currently archived: 92,100

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

34 (#471,489)

6 months
17 (#149,687)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Intuitionistic Logic Model Theory and Forcing.F. R. Drake - 1971 - Journal of Symbolic Logic 36 (1):166-167.
A note on intuitionistic models of ${\rm ZF}$.R. Lavendhomme & T. Lucas - 1983 - Notre Dame Journal of Formal Logic 24 (1):54-66.

Add more references