show/hide this revision's text 2 edited tags
show/hide this revision's text 1

Tarski-Grothendieck set theory, the axiom of pairing and the axiom of specification

I am building upon MO question 102846 concerning the Tarski-Grothendieck set theory (TG). I have two questions; 1/ I think that it is possible that the axiom of pairing (axiom 4 of the TG theory presented in question 102846) could be deleted. So, my question is: Is axiom 4 independant of the others axioms of the TG set theory ? 2/ In the considered question, it is asserted that the axiom of specification is a consequence of Tarski"s axiom A. My question is: what are the others axioms needed to have this result and could I have a proof ? Gérard Lang