The Axioms in My Understanding from Many Years of Experience

This is a discussion article that should raise more questions than answers. We write our own point of view about the concept of axioms. We list several examples, mostly known to readers, and focus on examples where the axioms produce separate areas of studies and applications. The classic definitions are schematically presented since these are well known. We briefly notice how they generated various other fields of development. Set theory is, in our opinion, the fundamental for new areas of development. Our focus is on some recent axioms such as uncertainty, probability, and new concepts and results related to these fields. The emphasis is on the meaning of an undefined concept and on its measuring.

Automated summary

This article discusses the concept of axioms, presenting examples and emphasizing how axioms generate separate areas of study and application. Throughout, the importance of set theory for new areas of development is highlighted, as well as the impact of recent axioms such as uncertainty and probability on related fields.