Talk:Tarski-Grothendieck set theory

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Is TG simply ZF minus Infinity, augmented by Tarski's axiom? Does that axiom also ensure the existence of infinite sets? What is known about the metamathematics of Tarski's axiom? Why is Grothendieck's name associated with TG? Has anyone written on TG outside of the Journal of Formalized Mathematics?132.181.160.42 03:38, 10 August 2006 (UTC)

This theory looks like very sloppy work to me, if this article correctly represents it. JRSpriggs 03:00, 21 August 2006 (UTC)

ad existence of infinite sets: yes, for any ordinal, Tarski's axiom gives you a limit ordinal containing it (http://mmlquery.mizar.org/mml/current/ordinal1.html#T51); the smallest containing the empty set is omega (http://mmlquery.mizar.org/mml/current/ordinal1.html#D12) JosefUrban 19:00, 8 June 2007 (UTC)

ad usage by Grothendieck: http://modular.fas.harvard.edu/sga/sga/4-1/4-1t_185.html;

and as for "sloppiness", I do not know how to measure this, but provided that this is used by two top-level mathematicians of 20. century, I'd be a bit cautious with such words (and if used at all, I'd certainly try to justify them) JosefUrban 19:09, 8 June 2007 (UTC)

[edit] Implies axiom of choice?

"Tarski's axiom implies the Axiom of Choice"

why/how?does anyone have a proof of this?

16:25, 28 March 2007 (UTC)

yes, a verified one: http://mizar.uwb.edu.pl/JFM/Vol1/wellord2.html (or in full detail: http://mmlquery.mizar.org/mml/current/wellord2.html#T26, http://mmlquery.mizar.org/mml/current/wellord2.html#T28). JosefUrban 18:15, 8 June 2007 (UTC)