> On 7 May 2018, at 12:52, Lawrence Crowell <[email protected]> > wrote: > > On Sunday, May 6, 2018 at 9:16:13 PM UTC-5, Russell Standish wrote: > On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: > > But don't you take all arithmetic theories to include the axioms that say > > every number has a successor? > > Just because every number has a successor does not entail the > existence of ω. > > This is otherwise known as "potential infinity" versus "actual > infinity". > > I've come across a similar sort of issue in studying what I call > "open dimensional systems". An open dimensional system is > still a finite dimensional system, but quite a distinct beast from the > usual fixed dimensional systems studied in dynamical systems > theory. Just doing a quick Google search indicates that I have been > unsuccessful in getting the term "open dimensional" adopted - it looks > like "unbounded dimensional" might have won the day :P. > > I will try to respond to Bruno more completely, but this is a bit of the > conundrum. One can work up various models with different ideas about > transfinite numbers. ZF set theory embraces infinity or transfinite numbers > with all the issues that come with it. Other ideas are more restrictive. From > the perspective of physics these concerns in a sense flap in the breeze with > little direct concern.
With mechanism, what can be proved, is that ZF and ZFC have the same opinion, about number’s theology (the G/G* logics, with quantifiers). Bruno > > LC > > > Cheers > -- > > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Senior Research Fellow [email protected] <javascript:> > Economics, Kingston University http://www.hpcoders.com.au > <http://www.hpcoders.com.au/> > ---------------------------------------------------------------------------- > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
