gjk@talcott.UUCP (Greg Kuperberg) (03/16/85)
Lambert Meertens has stated that he sees no justification for the Axiom of Choice. Well, that's odd, because I see no justification for not having it, and I particularly see no reason to have the Axiom of Determinism. Are you an A.D. fan, Mr. Meertens? Are there other A.D. fans out there? Are there A.D.ists and/or anti-A.C.ists out there who are not constructivists? --- Greg Kuperberg harvard!talcott!gjk "No Marxist can deny that the interests of socialism are higher than the interests of the right of nations to self-determination." -Lenin, 1918
play@mcvax.UUCP (Andries Brouwer) (03/18/85)
In article <362@talcott.UUCP> gjk@talcott.UUCP (Greg Kuperberg) writes: >Lambert Meertens has stated that he sees no justification for the Axiom of >Choice. Well, that's odd, because I see no justification for not having >it. Well, of course there is no other justification for assuming AC than that it is often convenient. But on the other hand, it is often inconvenient; one gets these strange paradoxes like that of Banach & Tarski, while it is possible to have a consistent theory of real analysis in which =each= set is Lebesgue measurable, if only one does not assume AC.
lambert@boring.UUCP (03/27/85)
> Lambert Meertens has stated that he sees no justification for the Axiom of > Choice. Well, that's odd, because I see no justification for not having > it, and I particularly see no reason to have the Axiom of Determinism. Are > you an A.D. fan, Mr. Meertens? Are there other A.D. fans out there? Are > there A.D.ists and/or anti-A.C.ists out there who are not constructivists? Sorry, if I am an A.D. fan, I am unaware of it, since I must confess I don't know what A.D. claims. (If Greg preaches the gospel to A.D. fans, he might achieve A.D. conversion :-) -- Sorry again, couldn't resist that. -- Lambert Meertens ...!{seismo,philabs,decvax}!lambert@mcvax.UUCP CWI (Centre for Mathematics and Computer Science), Amsterdam