3 papers
math.LO2026
On Weak Set Theories Interpreted in PA
Junhong Chen
We classify a broad family of weak first-order set theories, under ordinary parameter-free interpretability, by the first-order arithmetical theories with which they are mutually i…
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.LO2026
The Coding Conception of Set
Junhong Chen
We propose the Coding Conception of ordinals and sets, which takes Cantor's three generating principles as its sole foundation. Bounded sets of ordinals are generated synchronously…