Quantum groups under very strong axioms

Strong Fubini axioms from measure extension axioms

It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.

Strong axioms of in nity in NFU

Strong Axioms of Infinity and Elementary Embeddings

This is the expository paper on strong axioms of infinity and elementary embeddings origi;,ally to have been authored by Reinhardt and Solovay. It has been owed for some time and already cited with some frequency in the most recent set theoretical literature. However, for various reasons the paper did not appear in print far several years. The impetus for actual publication came from a series o...

Quantum Torsors with Fewer Axioms

We give a definition of a noncommutative torsor by a subset of the axioms previously given by Grunspan. We show that noncommutative torsors are an equivalent description of Hopf-Galois objects (without specifying the Hopf algebra). In particular, this shows that the endomorphism θ featuring in Grunspan’s definition is redundant.

Single Implicative Axioms for Groups and for Abelian Groups

Groups are usually deened by means of three axioms|the associative law, the existence of an identity element, and the existence of an inverse to each element. For abelian groups, the commutative law is included as a fourth axiom. However, it is well known that groups (also abelian groups) can be deened with a single equation. In 7], Tarski presented the single axiom x ? (y ? (z ? (x ? y))) = z ...