Abstract Concept of Changeable Set

TL;DR

This paper introduces the foundational theory of changeable sets, a formal framework for objects that can undergo continuous transformations and change properties based on perspective, with potential applications in physics and philosophy.

Contribution

It develops the formal theory of changeable sets, providing a new mathematical framework for modeling dynamic objects and perspectives.

Findings

Defines formal structure of changeable sets

Shows potential applications in physics of macrocosm

Lays groundwork for future theoretical developments

Abstract

The work lays the foundations of the theory of changeable sets. In author opinion, this theory, in the process of it's development and improvement, can become one of the tools of solving the sixth Hilbert problem least for physics of macrocosm. From a formal point of view, changeable sets are sets of objects which, unlike the elements of ordinary (static) sets may be in the process of continuous transformations, and which may change properties depending on the point of view on them (the area of observation or reference frame). From the philosophical and intuitive point of view the changeable sets can look like as "worlds" in which changes obey arbitrary laws.