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 so-called "inconsistent" number systems, that is, structures considered in a non-classical logic that allows at least some statements to be both true and false (bizarre, I know). He uses a three-valued logic containing true, false and a third value fruitfully interpreted as true-and-false, 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 well-known classical consistent complete subtheories."

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 so-called "inconsistent" number systems, that is, structures considered in a non-classical logic that allows at least some statements to be both true and false (bizarre, I know). He uses a three-valued logic containing true, false and a third value fruitfully interpreted as true-and-false, 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 well-known classical consistent complete subtheories."

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 so-called "inconsistent" number systems, that is, structures in a non-classical logic that allows at least some statements to be both true and false. He uses a three-valued logic containing true, false and a third value fruitfully interpreted as true-and-false. 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 well-known classical consistent complete subtheories."

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 so-called "inconsistent" number systems, that is, structures considered in a non-classical logic that allows at least some statements to be both true and false (bizarre, I know). He uses a three-valued logic containing true, false and a third value fruitfully interpreted as true-and-false, 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 well-known classical consistent complete subtheories."