What are Chris Mortensen number systems?
See the paper Chris Mortensen, Inconsistent Number Systems, Notre Dame Journal of Formal Logic, Volume 29, Number 1, Winter 1988. This paper continues the study of socalled "inconsistent" number systems, that is, structures considered in a nonclassical logic that allows at least some statements to be both true and false (bizarre, I know). He uses a threevalued logic containing true, false and a third value fruitfully interpreted as trueandfalse, but please see his paper for the details. He is particularly interested in finite structures in which all the classical theorems of PA remain true (and some of them also false). He writes, "it is one purpose of this paper to...[display] inconsistent theories which contain various wellknown classical consistent complete subtheories." 

