# 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