Consistent Positive and Linear Positive Quasi-antiorders

This investigation, in Bishop’s constructive mathematics in sense of well-known books [2], [3], [6] and Romano’s papers [9]-[15], is continuation of forthcoming Crvenkovic, Mitrovic and Romano’s paper [4], and the Romano’s paper [16]. Bishop’s constructive mathematics is developed on Constructive logic (or Intuitionistic logic ([19])) logic without the Law of Excluded Middle P ∨¬¬P . Let us note that in Constructive logic the ’Double Negation Law’ P ⇐⇒ ¬¬P does not hold, but the following implication P =⇒ ¬¬P holds even in Minimal logic.