On 12 Mar 2013, at 14:10, Stephen P. King wrote:
On 3/12/2013 8:58 AM, Stephen P. King wrote:
I have found a paper that seems to cover most of my thoughts about
arithmetic body problem:
Models of axiomatic theories admitting automorphisms
by A. Ehrenfeucht A. Mostowski
More on related concepts are found in the Vaught conjecture:
"The topological Vaught conjecture is the statement that whenever a
Polish group acts continuously on a Polish space, there are either
countably many orbits or continuum many orbits. The topological
conjecture is more general than the original Vaught conjecture:
countable language we can form the space of all structures on the
natural numbers for that language. If we equip this with the topology
generated by first order formulas, then it is known from A.
A. Mostowski, C. Ryall-Nardzewski, "Definability of sets of models of
axiomatic theories", Bulletin of the Polish Academy of Sciences
Mathematics, Astronomy, Physics), vol. 9(1961), pp. 163–7 that the
resulting space is Polish. There is a continuous action of the
symmetric group (the collection of all permutations of the natural
numbers with the topology of point wise convergence) which gives
the equivalence relation of isomorphism. Given a complete first order
theory T, the set of structures satisfying T is a minimal, closed
invariant set, and hence Polish in its own right."
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 solved, in the ideal "toy" case of
simple ideally correct machine, at the propositional level (that is:
the X, Z and S4Grz1) logics.
There might be a way, but it sounds to me like a very difficult
problem for expert in both provability logics and model theory. I
think you will need the diagonal algebra of Magari.
You will need to relate the work of the Italians, the Polish and the
Georgians, hmm... That is a work for the Russians (the
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 post to this group, send email to email@example.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.