外延公理:(Axiom of extensionality)兩個集合相同,若且唯若它們擁有相同的元素。
分類公理:(Axiom schema of specification / axiom schema of separation / axiom schema of restricted comprehension)或稱子集公理,給出任何集合及命題P(x),存在著一個原來集合的子集包含而且只包含使P(x)成立的元素。
配對公理:(Axiom of pairing)假如x, y為集合,那就有另一個集合{x,y}包含x與y作為它的僅有元素。
並集公理:(Axiom of union)每一個集合也有一個並集。也就是說,對於每一個集合x,也總存在著另一個集合y,而y的元素也就是而且只會是x的元素的元素。
Metamath (页面存档备份,存于互联网档案馆): A web site devoted to an ongoing derivation of mathematics from the axioms of ZFC and first-order logic. Principia Mathematica done right.
Mathias, A. R. D., 2004, "The Strength of Mac Lane Set Theory." Surveys, and sets out new results and new proofs for old results, for a number of alternatives to ZFC, including ZBQC (proposed by Saunders Mac Lane), topos theory, Kripke-Platek set theory, Foster-Kaye set theory, Harvey Friedman, and systems similar to 新基礎集合論.