On order types of linear basic algebras

Basic algebras form a common generalization of MV-algebras and of orthomodular lattices, the algebraic tool for axiomatization of many-valued Łukasiewicz logic and the logic of quantum mechanics. Hence, they are included among the socalled quantum structures. An important role is played by linearly ordered basic algebras because every subdirectly irreducible MV-algebra and every subdirectly irreducible commutative basic algebra is linearly ordered. Since subdirectly irreducible linearly ordered basic algebras exist of any infinite cardinality, the natural question is to describe all possible order types of these algebras. This problem is solved in the paper.