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reviewed Approve Cellular homology of the real projective space $\mathbb R P^n$
Jan
31
comment Theories of Arbitrary Morley Rank
The paper "The transcendental rank of a theory" of Lachlan is related to your question. The notion $\alpha_T$ is a little different to the Morley rank of $T$. But my impression is that every countable ordinal can be a Morley rank of some countable theory.
Jan
31
comment Theories of Arbitrary Morley Rank
Firstly, superstable does not imply Morley rank $< \infty$. $\omega$-stable does and is actually equivalent to Morley rank $< \infty$ for countable languages. Also for countable $\omega$-stable theories, Morley rank must be countable. This essentially follows from the fact that it equals to the Cantor Bendixson rank in the countable space $S(M)$ for an $\omega$-saturated $M$.
Jan
18
comment D.Marker's axiomatization of rings
The inverse of $x$ would be $0 - x$.
Jan
13
comment Definition for non-dividing
@kav11: well if 1) is true then 2) is true vacuously, since there are no infinite indiscernible sequences. Every sentence of the form $\forall x \in A ...$ is true if $A = \emptyset$. This should be clear for a logician.
Jan
13
comment Definition for non-dividing
As stated 1) implies 2). So nondividing is equivalent to 2). So your question says: is there a nice way of thinking about nondividing?
Jan
12
awarded  Custodian
Jan
12
reviewed Looks OK Concise Introduction to Galois Theory
Jan
12
reviewed Looks OK Description of norms on $\Bbb R$
Jan
12
reviewed Leave Open Description of norms on $\Bbb R$
Jan
12
answered When can independence of a statement in a theory be reduced to “truth”?
Jan
8
awarded  logic
Jan
7
comment Type of Infinite Tuple
Of course this all depends on how you define things. One way would be to say that $x_\alpha$ is not part of $T$ at all. $T$ has only first order sentences and each one can use only finitely many variables. Thus a fixed countable set of variables should suffice. $x_\alpha$ is certainly a part of the type. But there it is used as a free variable. If you want to view $tp(a)$ as a theory, then the new variables behave more like new constant. And indeed type is a consistent extension of $T$ in a new language (with new constant symbols).
Jan
7
answered Type of Infinite Tuple
Dec
10
answered Quantifier elimination in infinitary languages
Nov
23
awarded  Altruist
Nov
18
awarded  Investor
Oct
21
comment Proving that every interval in an o-minimal structure is definably connected.
Using o-minimality you can show that every definable interval in the second sense must have endpoints.
Sep
16
reviewed Approve Diophantine Equation or Ellipse
Sep
16
comment Shepherdson's model for Open Induction
It seems that the journal was last published in 1978. So there is little chance of finding the original article digitally. However some libraries will have physical copies in their archives. I'll be back at my uni in 2 weeks. If you don't find it by then, let me know and I'll try to get a copy and scan it for you.