Hypersets.

*(English)*Zbl 0756.03026Several elegant solutions of problems in theoretical computer science, e.g. the constructions of natural models of the \(\lambda\)-calculus by M. von Rimscha [Arch. Math. Logik Grundlagenforsch. 20, 65-73 (1980; Zbl 0428.03045)], have brought to the attention of a larger audience the usefulness of alternatives to the axiom of foundation. A systematic study of such principles (generalizations of Mostowski’s collapse combined with various forms of extensionality) has been initiated by P. Hajek [Z. Math. Logik Grundlagen Math. 11, 103-115 (1965; Zbl 0171.264)] and M. Boffa [ibid. 14, 329-334 (1968; Zbl 0169.306)]. In the paper under review the authors give an introduction into one of these alternatives, the antifoundation axiom AFA in P. Aczel’s terminology [Non-well-founded sets (1988; Zbl 0668.04001)]. The purpose of this paper is to convince the reader that AFA “is an interesting, mathematically and philosophically respectable alternative” to the axiom of foundation.

Reviewer: N.Brunner (Wien)

##### MSC:

03E65 | Other set-theoretic hypotheses and axioms |

03E75 | Applications of set theory |

03-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations |

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\textit{J. Barwise} and \textit{L. Moss}, Math. Intell. 13, No. 4, 31--41 (1991; Zbl 0756.03026)

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##### References:

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