Re: Toward a solution to the Arithmetic Body problem

2013-03-14 Thread Bruno Marchal
On 13 Mar 2013, at 17:37, Stephen P. King wrote: On 3/13/2013 12:22 PM, Bruno Marchal wrote: On 12 Mar 2013, at 18:54, Stephen P. King wrote: On 3/12/2013 12:22 PM, Bruno Marchal wrote: On 12 Mar 2013, at 14:10, Stephen P. King wrote: On 3/12/2013 8:58 AM, Stephen P. King wrote: Dear B

Re: Toward a solution to the Arithmetic Body problem

2013-03-13 Thread Stephen P. King
On 3/13/2013 12:28 PM, Bruno Marchal wrote: > > On 12 Mar 2013, at 19:31, Stephen P. King wrote: > >> I suspect that we need to look at the associativity properties of the >> algebra as per Kevin Knuth's work: http://arxiv.org/abs/1209.0881 > > > Really interesting, but hard to directly used fo

Re: Toward a solution to the Arithmetic Body problem

2013-03-13 Thread Stephen P. King
On 3/13/2013 12:22 PM, Bruno Marchal wrote: > > On 12 Mar 2013, at 18:54, Stephen P. King wrote: > >> On 3/12/2013 12:22 PM, Bruno Marchal wrote: >>> >>> On 12 Mar 2013, at 14:10, Stephen P. King wrote: >>> On 3/12/2013 8:58 AM, Stephen P. King wrote: > Dear Bruno, > >I have

Re: Toward a solution to the Arithmetic Body problem

2013-03-13 Thread Bruno Marchal
On 12 Mar 2013, at 19:31, Stephen P. King wrote: I suspect that we need to look at the associativity properties of the algebra as per Kevin Knuth's work: http://arxiv.org/abs/1209.0881 Really interesting, but hard to directlky used for the comp body problem, as it assumes too much physics.

Re: Toward a solution to the Arithmetic Body problem

2013-03-13 Thread Bruno Marchal
On 12 Mar 2013, at 18:54, Stephen P. King wrote: On 3/12/2013 12:22 PM, Bruno Marchal wrote: On 12 Mar 2013, at 14:10, Stephen P. King wrote: On 3/12/2013 8:58 AM, Stephen P. King wrote: Dear Bruno, I have found a paper that seems to cover most of my thoughts about the arithmetic body

Re: Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Stephen P. King
On 3/12/2013 1:54 PM, Stephen P. King wrote: >> Let me refine my concerns a bit. Is there a method to consider the >> >> Vaught conjecture on finite lattice approximations of Polish spaces? >> >> Please relate all this, as formally as in the Ehrenfeucht Mostowski >> paper, to what has already been

Re: Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Stephen P. King
On 3/12/2013 12:22 PM, Bruno Marchal wrote: > > On 12 Mar 2013, at 14:10, Stephen P. King wrote: > >> On 3/12/2013 8:58 AM, Stephen P. King wrote: >>> Dear Bruno, >>> >>> I have found a paper that seems to cover most of my thoughts >>> about the >>> arithmetic body problem: >>> Models of axio

Re: Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Bruno Marchal
On 12 Mar 2013, at 14:10, Stephen P. King wrote: On 3/12/2013 8:58 AM, Stephen P. King wrote: Dear Bruno, I have found a paper that seems to cover most of my thoughts about the arithmetic body problem: Models of axiomatic theories admitting automorphisms by A. Ehrenfeucht A. Mostowski ht

Re: Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Stephen P. King
On 3/12/2013 9:27 AM, Richard Ruquist wrote: > Steve, > Does not the wiki ref imply "that the number of countable models of a > first-order complete theory in a countable language is finite" or Xo? > Richard Hi Richard, Yes, "the number of countable models of a first-order complete theory

Re: Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Richard Ruquist
Steve, Does not the wiki ref imply "that the number of countable models of a first-order complete theory in a countable language is finite" or Xo? Richard On Tue, Mar 12, 2013 at 8:58 AM, Stephen P. King wrote: > Dear Bruno, > > I have found a paper that seems to cover most of my thoughts

Re: Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Stephen P. King
On 3/12/2013 8:58 AM, Stephen P. King wrote: > Dear Bruno, > > I have found a paper that seems to cover most of my thoughts about the > arithmetic body problem: > Models of axiomatic theories admitting automorphisms > by A. Ehrenfeucht A. Mostowski > http://matwbn.icm.edu.pl/ksiazki/fm/fm4

Toward a solution to the Arithmetic Body problem

2013-03-12 Thread Stephen P. King
Dear Bruno, I have found a paper that seems to cover most of my thoughts about the arithmetic body problem: Models of axiomatic theories admitting automorphisms by A. Ehrenfeucht A. Mostowski http://matwbn.icm.edu.pl/ksiazki/fm/fm43/fm4316.pdf More on related concepts are found in the V