Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století

Abstract

Vopěnka’s Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem’s construction of a nonstandard model of arithmetic, and its inception has been explicitly mentioned as an attempt to axiomatize Robinson’s nonstandard analysis. Vopěnka preferred working in an axiomatic theory to investigating its individual models; he also viewed other areas of nonclassical mathematics through this prism. This article is a contribution to the mapping of the mathematical neighbourhood of the Alternative Set Theory, and at the same time, it submits a challenge to analyze in more detail the genesis and structure of the philosophical links that eventually influenced the Alternative Set Theory.

Keywords

• petr vopěnka
• alternative set theory
• nonstandard analysis
• philosophy of mathematics
• nonclassical mathematics
• logic
• axiomatic theory