3 papers
math.LO2026
A new kind of anti-foundation axioms
Daheng Ju
Among the four well-known anti-foundation axioms, , , , and , the latter three are all special cases of $\mathsf{AFA}^\si…
math.LO2026
Frucht's theorem and other set-theoretic principles below the axiom of choice and the axiom of foundation
Junhong Chen, Daheng Ju
We take the first step toward the study of set-theoretic principles below the axiom of choice and the axiom of foundation by studying Frucht's theorem,…
math.LO2024
Comparing Anti-foundation Axioms by Comparing Identity Conditions for Sets
Daheng Ju, Qihang Jing
In non-well-founded set theory, which anti-foundation axiom is philosophically justified, BAFA, FAFA, SAFA, AFA, or some other? In this paper, we investigate a general approach to…