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From: Chris Menzel on 18 Apr 2005 18:49 On Mon, 18 Apr 2005 14:37:00 -0400, Will Twentyman <wtwentyman(a)read.my.sig> said: > It seems that many people prefer the continuum hypothesis being true. My impression some 15 years ago when I was studying set theory more seriously was that most working set theorists believed (G)CH to be false, largely because the power set operation is too "rich" in one way or another only to bump you to the very next infinite cardinality. I don't know if this is still the general view of the matter.
From: Bill Smythe on 18 Apr 2005 19:12 "Chris Menzel" wrote: > My impression some 15 years ago when I was studying set theory more > seriously was that most working set theorists believed (G)CH to be > false, largely because the power set operation is too "rich" in one way > or another only to bump you to the very next infinite cardinality. I > don't know if this is still the general view of the matter. Um, isn't it known that either (G)CH or its negation would be consistent with the basic axioms of set theory? If that's the case, then nobody is going to have a "view" on whether (G)CH is true or false. One would, instead, have a view on whether it is DESIRABLE. Bill Smythe
From: Chris Menzel on 18 Apr 2005 19:25 On Mon, 18 Apr 2005 18:12:08 -0500, Bill Smythe <chichess(a)beforeRCNafter.com> said: > "Chris Menzel" wrote: >> My impression some 15 years ago when I was studying set theory more >> seriously was that most working set theorists believed (G)CH to be >> false, largely because the power set operation is too "rich" in one >> way or another only to bump you to the very next infinite >> cardinality. I don't know if this is still the general view of the >> matter. > > Um, isn't it known that either (G)CH or its negation would be consistent > with the basic axioms of set theory? Yes, very well known (assuming ZF is itself consistent). > If that's the case, then nobody is going to have a "view" on whether (G)CH > is true or false. You're quite wrong about that. Many set theorists have such a view. > One would, instead, have a view on whether it is DESIRABLE. Not if one thinks that sentences in the language of set theory are all either true or false in the universe of sets, irrespective of the question of their decidability in ZF. Chris Menzel
From: Will Twentyman on 18 Apr 2005 21:40 Chris Menzel wrote: > On Mon, 18 Apr 2005 14:37:00 -0400, Will Twentyman > <wtwentyman(a)read.my.sig> said: > >>It seems that many people prefer the continuum hypothesis being true. > > > My impression some 15 years ago when I was studying set theory more > seriously was that most working set theorists believed (G)CH to be > false, largely because the power set operation is too "rich" in one way > or another only to bump you to the very next infinite cardinality. I > don't know if this is still the general view of the matter. > I was careful not to say "most" because I have no idea what the percentages might be. -- Will Twentyman email: wtwentyman at copper dot net
From: Chris Menzel on 18 Apr 2005 23:38
On Mon, 18 Apr 2005 21:40:50 -0400, Will Twentyman <wtwentyman(a)read.my.sig> said: > > Chris Menzel wrote: >> On Mon, 18 Apr 2005 14:37:00 -0400, Will Twentyman >> <wtwentyman(a)read.my.sig> said: >> >>>It seems that many people prefer the continuum hypothesis being true. >> >> My impression some 15 years ago when I was studying set theory more >> seriously was that most working set theorists believed (G)CH to be >> false, largely because the power set operation is too "rich" in one way >> or another only to bump you to the very next infinite cardinality. I >> don't know if this is still the general view of the matter. >> > > I was careful not to say "most" because I have no idea what the > percentages might be. Right, I noticed that; my remark was only intended as a supplement to yours, not a correction. Sorry if that wasn't clear. |