  Vop\v{e}nka'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. Vop\v{e}nka 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.
