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Mar
31
comment Definition of dicrete ordering
A ordering is usually called discrete if every element $x$ except the top one has an immediate successor $s(x)$, (i.e. $x < s(x)$ and there is nothing in between) and every element $y$ except the bottom one has an immediate predecessor $p(y)$ (i.e. $p(y) < y$ and there is nothing in between)
Mar
28
comment The unique model of cardinal $\kappa$ of a $\kappa$-categorical countable theory is saturated.
The proof you give is more or less the proof I know. I believe it is the standard proof. I can also imagine contexts where Theorem 1 and $\omega$-stable implies $\kappa$-stable can be referred as "pretty easy".
Mar
21
comment isomorphism between divisible, totally ordered, abelian groups
Also from model theoretical point of view, any theory with an order is unstable and hence has $2^\lambda$ nonisomorphic models in an uncountable cardinality $\lambda$.
Mar
19
comment Extending Henkin's Theorem to Completeness in Marker's Text
I don't think there is an easy way to obtain completeness from compactness. For one thing compactness theorem does not mention any proof system. Not all proof systems are complete, so you can't obtain completeness without making your hands dirty (i.e. without analysing your proof system).
Mar
19
comment Extending Henkin's Theorem to Completeness in Marker's Text
So why do you think it should be proved without using the completeness theorem?
Mar
19
comment Extending Henkin's Theorem to Completeness in Marker's Text
I had a brief look at the beginning of chapter 2 of Marker's book. As far as I can see, he does not attempt to prove Goedel's completeness theorem. Does he use the lemma you mention in the text?
Mar
17
comment Omitting types and real closed fields
A countable complete theory has a prime model if and only if isolated types are dense. In case of o-minimal theories, one shows by induction on $n$ that isolated types are dense in $S_n(A)$ (for every set $A$). If I remember it correctly, the induction step works for all theory, whereas for $n=1$ you need o-minimality. Actually this shows that an o-minimal theory has prime models over every subset (just like an $\omega$-stable theory).
Mar
14
answered Omitting types and real closed fields
Mar
1
answered Order of ab when <a> and <b> are distinct
Feb
25
answered Problem with Diophantine equation
Feb
15
comment Show that the following sequence, if $n>12, $ $|a_n-L|<\frac{1}{n}$.
If $n > 12$, then $4(4n-3) = 16n - 12 > 15n$.
Feb
11
reviewed Approve suggested edit on Proving an integral using a series
Feb
4
comment Models of $T_{\forall\exists}$ embed in a existentially closed extension model of $T$.
That is exactly how you proceed.
Feb
4
answered Models of $T_{\forall\exists}$ embed in a existentially closed extension model of $T$.
Feb
3
comment What $P(E)\sim (E \to \{ 0,1\} )$ mean?
I suspect it is the set of functions from $E$ to $\{0, 1\}$.
Jan
29
reviewed Approve suggested edit on Method of Moments Estimation over Uniform Distribution
Jan
29
answered Algebraic types are isolated
Jan
22
reviewed Approve suggested edit on Ques from exam: sequence of functions and improper integrals
Jan
20
answered Problem concerning formally real fields
Jan
16
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