Expressing infinity without foundation

Franco Parlamento, Alberto Policriti
1991 Journal of Symbolic Logic (JSL)  
The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.
doi:10.2307/2275470 fatcat:jr5hzqybvbd47c5jurv7mutzva