Non-well-founded Sets Research Articles

An Application of Non‐Wellfounded Sets to the Foundations of Geometry

An Application of Non‐Wellfounded Sets to the Foundations of Geometry

Nonstandard set theory

AbstractNonstandard set theory is an attempt to generalise nonstandard analysis to cover the whole of classical mathematics. Existing versions (Nelson, Hrbáček, Kawai) are unsatisfactory in that the unlimited idealisation principle conflicts with the wish to have a full theory of external sets.I re-analyse the underlying requirements of nonstandard set theory and give a new formal system, stratified nonstandard set theory, which seems to meet them better than the other versions.

Book review: Peter Aczel. Non-well-founded sets.

Book review: Peter Aczel. Non-well-founded sets.

An elementary variant of nonstandard set theory

An elementary variant of nonstandard set theory