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Mar
30
awarded  model-theory
Mar
29
awarded  Enlightened
Mar
29
awarded  Nice Answer
Feb
19
comment Symmetry of Forking
I think now 1) is weaker than it needs to be. It needs to assert that $O_p$ is unique. I.e. when you look at ideal extensions of $p$ under the action of $A$-conjugation, there is one and only one orbit that has bounded size.
Feb
19
comment Symmetry of Forking
Correction: in 1) the ideal extension $\mathbb p$ is not unique. Any $A$-conjugate of $\mathbb p$, of which there may be $2^{|T|}$, will do.
Feb
6
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