Sentence examples for based on intuitionistic logic from inspiring English sources

Therefore we can not assume AC in any reasonable ZF set theory based on intuitionistic logic.

As a consequence, foundation, as usually formulated, can not be part of a ZF set theory based on intuitionistic logic.

Although there are many systems of sets based on intuitionistic logic, we can distinguish two main trends within the literature.

Goodman and Myhill give an argument for set theories based on intuitionistic logic (Goodman and Myhill 1978).

When introducing versions of ZF based on intuitionistic logic, the first step is to eliminate from the logic the principle of the excluded middle (EM).

They were introduced in the 1970's and they represent a formal context within which to codify mathematics based on intuitionistic logic (see the entry on constructive mathematics).

This theory is both predicative (so that in particular it lacks a type of propositions), and based on intuitionistic logic[2].

Around the turn of this century, Veldman (Veldman 2005), in the Netherlands, and Ishihara (Ishihara 2005, 2006), in Japan, independently initiated a programme of constructive reverse mathematics (CRM), based on intuitionistic, rather than classical, logic.

Then, the image is modeled based on intuitionistic fuzzy set [47].

Anti-realists follow verificationists in rejecting the intelligibility of such states of affairs and tend to base their rules for assertion on intuitionistic logic, which rejects the universal applicability of the Law of Bivalence (the principle that every statement is either true or false).

One could imagine a geometry based not on classical logic, but, e.g., on intuitionistic logic, where principles such as the excluded third, i.e., \(p\) or not-\(p\), for any statement \(p\), or double negation, i.e., if not-not-\(p\) then \(p\), no longer hold.