Errata

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\usepackage[centertags]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \title{The Structure of Models of Peano Arithmetic: Errata}

\begin{document} \maketitle \begin{itemize} \section{Corrections} \item p. vii, l. -3: Should be: ``type UNIQ14f653679d6b6acf-MathJax-3-QINU..." \item p. 21, Exercise 1.14.5: UNIQ14f653679d6b6acf-MathJax-4-QINU should be UNIQ14f653679d6b6acf-MathJax-5-QINU \item p. 22, l. -12: [70] should be [71] \item p. 23, l. 19: [209] refers to a paper of A. Wilkie, it should refer to George Wilmer's thesis which is missing in the references. \item p. 48, l. 3: the second instance of 2.3.2 should be 2.3.4. \item p. 57, Proof of Corollary 3.1.17. Should be ``Theorem 3.1.16..." To finish the argument one also needs to evoke Theorem 2.1.1. \item p. 85, Exercise 3.6.17: Delete the hint. \item p.98, l.-3: In the first line of the displayed formula, UNIQ14f653679d6b6acf-MathJax-6-QINU should be replaced by UNIQ14f653679d6b6acf-MathJax-7-QINU . The same change should be made in the second line. \item p.106, paragraph starting with l. -9: Replace the third sentence with: ``Let UNIQ14f653679d6b6acf-MathJax-8-QINU be the set of meet-irreducibles." Then at the end of the paragraph replace the last part of the last sentence starting with ``. . . containing UNIQ14f653679d6b6acf-MathJax-9-QINU. . ." with ``. . . containing UNIQ14f653679d6b6acf-MathJax-10-QINU , which is UNIQ14f653679d6b6acf-MathJax-11-QINU." \item p. 109, Theorem 4.5.5: Definition of UNIQ14f653679d6b6acf-MathJax-12-QINU is missing. Before the theorem insert: ``If UNIQ14f653679d6b6acf-MathJax-13-QINU and UNIQ14f653679d6b6acf-MathJax-14-QINU are representations, the product UNIQ14f653679d6b6acf-MathJax-15-QINU is a function UNIQ14f653679d6b6acf-MathJax-16-QINU defined by UNIQ14f653679d6b6acf-MathJax-17-QINU iff UNIQ14f653679d6b6acf-MathJax-18-QINU and UNIQ14f653679d6b6acf-MathJax-19-QINU. Then UNIQ14f653679d6b6acf-MathJax-20-QINU and UNIQ14f653679d6b6acf-MathJax-21-QINU." \item p.110/l.15: Should be: UNIQ14f653679d6b6acf-MathJax-22-QINU. \item p.110/l.18: Delete “UNIQ14f653679d6b6acf-MathJax-23-QINU”. \item p. 118, l. 12: Near end of last line of the Theorem, delete the extraneous “) ” \item p.128/Lemma 4.7.4: Interchange “UNIQ14f653679d6b6acf-MathJax-24-QINU” and “UNIQ14f653679d6b6acf-MathJax-25-QINU”. \item p.152/l.21: Expression at end of line should be: UNIQ14f653679d6b6acf-MathJax-26-QINU. \item p. 159, l. -1. UNIQ14f653679d6b6acf-MathJax-27-QINU \item p. 159. Lemma 6.2.5. Delete the last part on the last sentence starting with ``and if..." \item p. 177, l. -12: UNIQ14f653679d6b6acf-MathJax-28-QINU should be UNIQ14f653679d6b6acf-MathJax-29-QINU \item p. 179, l. -12: [132] should be [130] \item p. 179, l. -8: should [166] be J. Schmerl, Peano models with many generic classes. Pacific Journal of Mathematics 46, 523-536 (1973). This entry is missing in the references. \item p. 182, Proposition 7.1.3: UNIQ14f653679d6b6acf-MathJax-30-QINU is supposed to be just a cut, but it should be also assumed to be closed under addition and multiplication \item p. 246. Lemma 9.4.3 (1). One has to assume that UNIQ14f653679d6b6acf-MathJax-31-QINU and UNIQ14f653679d6b6acf-MathJax-32-QINU are not infimum and supremum of the same gap. \item p. 292, Question 17 is garbled. It should say: Suppose UNIQ14f653679d6b6acf-MathJax-33-QINU is countable recursively saturated and UNIQ14f653679d6b6acf-MathJax-34-QINU is such that UNIQ14f653679d6b6acf-MathJax-35-QINU. Is there a countable recursively saturated UNIQ14f653679d6b6acf-MathJax-36-QINU such that UNIQ14f653679d6b6acf-MathJax-37-QINU, and if UNIQ14f653679d6b6acf-MathJax-38-QINU is coded in UNIQ14f653679d6b6acf-MathJax-39-QINU, then UNIQ14f653679d6b6acf-MathJax-40-QINU? \section{Typos} \item p. vi, l. 7: fragment = fragment of \item p. vi, l. -17: While, = While \item p. vi, l, -9: proves = and proves \item p. vi, l. -2 f.b.: purpose = purpose of \item p. vii, l. -9: delete ``and" \item p. vii, l. -2 f: For every countable model UNIQ14f653679d6b6acf-MathJax-41-QINU, the isomorphism type if its reducts... \item p. viii, l. -14: the Chapter 7 = Chapter 7 \item p. 1, l. 3: delete ``a'' \item p. 3, l. -11: is UNIQ14f653679d6b6acf-MathJax-42-QINU = UNIQ14f653679d6b6acf-MathJax-43-QINU is \item p. 3, l. -4: UNIQ14f653679d6b6acf-MathJax-44-QINU = UNIQ14f653679d6b6acf-MathJax-45-QINU \item p. 8, l. -5: UNIQ14f653679d6b6acf-MathJax-46-QINU = UNIQ14f653679d6b6acf-MathJax-47-QINU \item p. 14, Definition 1.9.1: ``partial inductive satisfaction class''should be in italics \item p. 14, l. -9 and 7: instead of Con(Th(UNIQ14f653679d6b6acf-MathJax-48-QINU) one should read ``Th(UNIQ14f653679d6b6acf-MathJax-49-QINU is consistent'' \item p. 19, l. 14: proof the = proof of the \item p. 24, l. 13: [69] . = [69]. \item p. 24, l. 17: Kotlarski and Kaye = Kaye and Kotlarski \item p. 25, l. 1: models arithmetic = models of arithmetic \item p.27, l.22: In Corollary 2.1.4, last word of first line should be “end”, not “and”. \item p. 32, l. 7: the contrary = to the contrary \item p. 33, l. -5: replaced = replaced by \item p. 33, l. 4 f.b.: single = a single \item p. 48, l. 15: Wikie = Wilkie \item p. 49, l. -6: each of which = each element of which \item p. 51, l. 7: UNIQ14f653679d6b6acf-MathJax-50-QINU should be UNIQ14f653679d6b6acf-MathJax-51-QINU (similarly for p. 51, l. 9) \item p. 51, l. 17: unboounded = unbounded \item p. 52, l. 21: infinte = infinite \item p. 53, l. 2: type = types \item p. 54, l. 6: do not look = do not look the same \item p. 55, l. 11: the another = another \item p. 57, l. 14: realizes = realize \item p. 57, l. -10: Should be ``Theorem 3.1.16..." \item p. 57, l. -7; Should be ``UNIQ14f653679d6b6acf-MathJax-52-QINU... \item p. 58, l. 10: since UNIQ14f653679d6b6acf-MathJax-53-QINU, is rare = , since UNIQ14f653679d6b6acf-MathJax-54-QINU is rare \item p. 60, l. 13: gap(b)UNIQ14f653679d6b6acf-MathJax-55-QINUgap(b) = gap(b) \item p. 60, all UNIQ14f653679d6b6acf-MathJax-56-QINU's in the lines -8,-7, and -6 should be UNIQ14f653679d6b6acf-MathJax-57-QINU's. \item p. 61, l. 3 UNIQ14f653679d6b6acf-MathJax-58-QINU should be UNIQ14f653679d6b6acf-MathJax-59-QINU. \item p. 61, l. -5 : The are = There are \item p. 67, l. -18: types. = types, \item p. 67, l. -17: Then = then \item p. 80, l. 7: UNIQ14f653679d6b6acf-MathJax-60-QINU = UNIQ14f653679d6b6acf-MathJax-61-QINU \item p. 85, Exercise 3.6.25: are = There are \item p. 87, Definition after 3.6.38 should be UNIQ14f653679d6b6acf-MathJax-62-QINU, not UNIQ14f653679d6b6acf-MathJax-63-QINU. \item p. 100, l. 18: Should be UNIQ14f653679d6b6acf-MathJax-64-QINU \item p. 107, l. 3: Theorem 4.5.32 = Corollary 4.5.32 \item p. 107, l. -16: represenatation \item p. 107, l. -3: UNIQ14f653679d6b6acf-MathJax-65-QINU should be UNIQ14f653679d6b6acf-MathJax-66-QINU. \item p. 108, l. 23: be list all = be a list of all \item p. 109. l. 4: Should be ``The inclusion UNIQ14f653679d6b6acf-MathJax-67-QINU..." \item p. 122, l. -15: used get = used to get \item p. 124, l. 14: hold for = hold for \item p. 125, l. -17: the tree = on the tree \item p. 128, l. -9: represenations \item p. 131, l. 3: (see Exercise 4.8.2) \item p. 133, l. 8: charaterization \item p. 135, l. 7: introduced \item p. 142, l. 1: there some = there exists some \item p. 145, l. 2: instead = instead of ? \item p. 151, l. 17: is not be = is not \item p. 152, l. 17: off = of \item p. 156, l. -18: linearly set = linearly ordered set \item p. 157, l. 17: Theorems 5.3.4 = Theorem 5.3.4 \item p. 162, l. 10,12: Theorem 6.2.6 = Lemma 6.2.6 \item p. 166, l. -10: funtcions \item p. 168, l. -6: would no = would be no \item p. 169, second line of Theorem 6.4.3: UNIQ14f653679d6b6acf-MathJax-68-QINU \item p. 171, l. 10: the proof = of the proof \item p. 173. First line of Theorem 6.4.8: UNIQ14f653679d6b6acf-MathJax-69-QINU. \item p. 177, l. -14: possibilities \item p. 177, l. -5: not = are not \item p. 179, l. -14: independently \item p. 184, l. -4: Propositional = Proposition \item p. 189, l. -11: Theorem 2.2.8 = Theorem 2.2.16 \item p. 191, l.-8: Should be UNIQ14f653679d6b6acf-MathJax-70-QINU \item p. 192, l. 8: if = of \item p. 194, l. -6: Theorembut = Theorem but \item p. 197, l. 12: model IA = model of IA \item p. 200, l. -10: which = which is \item p. 201, l. -12: models = models of \item p. 203, l. 10: UNIQ14f653679d6b6acf-MathJax-71-QINU \item p. 206, l. 10: model = models \item p. 209, Fourth line of the proof of Corollary 8.4.6: UNIQ14f653679d6b6acf-MathJax-72-QINU \item p. 214, l. -17: than least = than the least \item p. 221, l. -12: delete ``a'' \item p. 222, l. 5: Corollary 3.2.4 = Lemma 3.2.4 \item p. 225, l. 7: maximal = a maximal \item p. 227, l. 12: Corollary 8.1.2 = Proposition 8.1.3. Delete the statement in parenthesis. \item p. 227, l. -10: Back-and-forth, = Back-and-forth \item p. 228, l. 20 f.b.: Frederike = Friederike \item p. 229, l. 9: proof the = proof of the \item p. 229, l. -14: the question mark appears ``upside down'' \item p. 233, l. 12: aid = and \item p. 234, l. 8: Proposition 9.1.3 = Lemma 9.1.3 \item p. 235, l. 2: models = model \item p. 239, l. 13: index if = index of \item p. 250, l. -6 f: realizes = realize \item p. 253, l. -7: of countable = of a countable \item p. 254, l. 14: definiton \item p. 267, l. -12: devoted the = devoted to the \item p. 268, l. 6: delete ``an'' \item p. 276, l. -1: Use previous = Use the previous \item p. 280, l. 11: theory = theory of \item p. 284, l. 5: is get = is to get \item Reference [36]: G\"{o}tenborg = G\"{o}teborg \item Reference [43]: add ``{\it Mathematical Logic and Foundations of Set Theory} (Proc. Internat. Colloq., Jerusalem, 1968)'' \item Reference [54]: add ``Volume 1292 of {\it Lecture Notes in Mathematics}'' \item Reference [83]: of 619 = 619 of \item Reference [85]: delete ``(1983)''; this reference should appear after reference [88] \item Reference [109]: od = of \item Reference [113]: of pa = of UNIQ14f653679d6b6acf-MathJax-73-QINU \item Reference [120]: add `` in Automorphisms of first-order structures, R. Kaye, D. Macpherson (eds.)'' \item Reference [148]: {\bf CIII} = {\bf 103} \item Reference [153]: charaterization \item Reference [164]: add ``Volume 859 of {\it Lecture Notes in Mathematics}'' \item Reference [167]: add ``Stud. Logic Found. Math., 120'' \item Reference [172]: add ``Lecture Notes Logic, 12'' \item Reference [188]: Unmglichkeit = Unm\"{o}glichkeit; vollstndigen = vollst\"{a}ndigen \item Reference [189]: abzhlbar = abz\"{a}hlbar; Fundam. = Fund. \item Reference [199]: add ``Volume 834 of {\it Lecture Notes in Mathematics}'' \item Reference [204]: poljak-r\"{o}dl = Poljak-R\"{o}dl \item Reference [206]: the name of the journal is usually abbreviated as ``Algebra Logic Appl.'' \item Reference [208]: complete = complete models \item Reference [212]: add ``Proceedings of the International Congress of Mathematicians'' \end{itemize} \end{document}

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