Model Theory: an Introduction
Errors
There are a number of errors in the text. Here are some of
the most misleading ones that I am aware of.
- Introduction
- page 1: The statement of Morley's Theorem should say "... then T has a unique
model of cardinality lambda for all uncountable lambda"
- Chapter 1
- page 8 line -10: $e^G=1$ should be $e^G=0$.
- pag2 26 line 14: $G_A \models \psi(a,b...$
- page 30 ex. 1.4.10 part a) should say that x is
A-definable if and only if there is a 0-definable X,
a 0-definable f:X->M and a in A with f(a)=x, while
in c) Show dcl(dcl(A))=dcl(A).
- Chapter 2
- pg 35: definition 2.1.5 should say $\exists v\ \phi(v)\rightarrow \phi(c)\in T$
- pg 35: The definition of ~ should be c~d if c=d is in T.
- pg 42: the second line of the proof of 2.2.8 should begin:
"Because T is complete,..."
- pg 59: In the statement of Scott's Theorem:
Both M and N should be countable!
- Exercise 2.5.17 a) N should be a model of T.
- Exercise 2.5.20 Take the filter generated by D
- Chapter 3
- page 80 line 19-20:k_0=max{h_i/m_i: m_i>0} and k_1=
min{h_i/m_i:m_i<0}
- page 88: Cor 3.2.9 X is definable
- page 89 line 5: the q_i generate I
- page 89 line 15: Clearly I(V(J))\supseteq J.
- page 86 Lemma 3.2.4 iii) X should be a proper subset of Y
and I(Y) should be a proper subideal
- page 88: Corollary 3.2.9 X should be definable
- page 93: line 9 f_i:X_i--> K^{l_i}
- page 98: 3.3.19 "the closure of A is semialgebraic"
- page 98: Corollary 3.3.20: X should be "semialgebraic, closed and bounded"
- page 101 last line of cor 3.3.26: should be "then f(a)=f(b). We call f..."
- page 101 line -13,-12: "...then \exists z (x,g(x),z) in X....
h(x)=(g(x),f(x,g(x)).
- page 101: case 3 d+c/2
- page 101 last line \bar y should be in X
- page 102: line -5 "infinite" should be "finite"
- page106: line -2 "irreducible" should be "reducible
- page 109: 3.4.28 Assume I is prime
- pagd 110: 3.4.33a) H should be definable, a second part to a) should
ask you to next conclude that H={0} or H=G.
- page 112: the assumption in Shanuel's Conjecture: should be "linearly independent over
Q".
- page 112: in the statement of the Ax-Kochen theorem
we need to assume that the residue fields have characteristic
0 or are unramified.
- Chapter 4
- pg 115: Def 4.1.1: Let p be a set...
- pg 117: line 5 \bar a in N
- pg 119 line 6: [phi and psi]=[phi] union [psi]
- pg 130 the first displayed line in the proof of 4.2.9 should
be (exists w phi(v,w))--> psi(v)
- pg 132 line -11: the union should be an intersection
- pg 133 line 4: |[phi and not psi]| is uncountable for some i
- pg 137 line 2: M models exists v phi(v,a)
- pg 147 line 2: a in X
- pg 148: Def 4.3.29 the order of g is less than the order of f.
- pg 149: in the proof of 4.3.30 there are many places where
a^n should be a^(n).
- pg 151: Definition 4.3.35 delete "if" in the last line of the
definition.
- pg 153: claim 1 : delete "is realized in N_0"
- pg 166: 4.5.23 Assume N is interpretable in M.
- pg 164: Exercise 4.5.13 Sigma should have free variables
v_1,...,v_n
- pg 165 Exercise 4.5.18: Assume kappa is uncountable.
- Chapter 5
- pg 178: the definition of indiscernibles
should end "for all formulas \phi in n free variables"
- lemmas 5.4.3 and 5.4.4 are full of typos. Here is a better version.
- pg 202: in 5.5.5 M should be countably infinite
- Chapter 6
- 6.1.17 should say "Suppose T has no Vaughtian pairs,
M models T, and X subset M^n is infinite and definable. If
N is a proper elementary submodel of M and X is N-definable,
then X is not a subset of N^n."
- pg 223 line 3:
"...definable subsets Y_1,Y_2,... of X such that each Y_i
has Morley rank beta."
- pg 245: In the definition of the Cantor-Bendixson derivative
in part iii) we should take intersections instead of unions.
In g) of the problem p should be in \Gamma^\alpha(X)-\Gamma^(\alpha+1)(X).
- Chapter 8
- pg 295: in the proof of 8.2.7 choose phi
to have degree 1.
- Appendix B:
The proof of B.14 is much too quick. Here
is a better version.
Revised 6/16/06