Isomorphic Subtypes in a Finite Generalized Ordered Type
We give sufficient conditions to find all subtypes isomorphic to a subtype in a finite generalized ordered type.
math.LO↗
arXiv subjects
Jean S. Joseph
Publications and source records attributed to Jean S. Joseph.
Axioms for the Real Numbers: A Constructive Approach
We present axioms for the real numbers by omitting the field axioms and then derive the field properties of the real numbers. We prove all our theorems constructively.
math.LO↗
On Generalized Ordered Sets: A constructive development
We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual weak order causes problems on the real numbers because their strict order cannot be proved to be trichotomous.
math.LO↗
The Surreal Numbers as an Ordered Commutative Ring with an Apartness: A Development in Univalent Foundations
We define a multiplication on the surreal numbers as higher inductive-inductive types.
math.LO↗