Pub Date : 2008-06-01DOI: 10.1017/S1079898600001748
Robert S. Lubarsky
that expressions like ‘brother’ and ‘male sibling’ may be translated into the same expression of another language that has only one phrase for the concept while preserving sense. Salmon proposses to resolve the conflict by abandoning Church’s solution to the paradox, noting that doing so appears to undermine the original impetus behind Frege’s distinction between Sinn and Bedeutung. The very possibility of language also discusses Church’s Translation Argument, arguing that the moral of that argument shows that Dummett’s account of language collapses into the absurd position that it is impossible for us to know a language. The volume contain a helpful bibliography of Salmon’s writings from1979–2005. Unfortunately, there is no bibliography of the works cited; the details are included only in footnotes. There is a good deal of cross-referencing amongst the included papers; regrettably, these references refer to other papers that appear in the collection by their original pagination. Furthermore, cross-references to footnotes internal to an individual paper seem not always to have been updated when changes to the text affected the numbering of the notes. The text is well bound, attractively if densely type-set, and relatively free from typographical errors. Happily, those that exist are easily rectified. Brian van den Broek Department of Philosophy, University of Manitoba, Winnipeg, Manitoba, R3T 2M8, Canada. broek@cc.umanitoba.ca.
像“兄弟”和“兄弟姐妹”这样的表达可能被翻译成另一种语言的相同表达，这种语言只有一个短语来表达这个概念，同时保留了意义。萨尔蒙建议通过放弃丘奇对悖论的解决方案来解决冲突，他指出，这样做似乎破坏了弗雷格区分“罪”和“罪”背后的原始动力。语言的可能性也讨论了丘奇的翻译论点，认为该论点的道德表明，达米特对语言的描述陷入了荒谬的境地，即我们不可能了解一种语言。这本书包含了萨尔蒙1979 - 2005年著作的参考书目。不幸的是，没有引用作品的参考书目;细节只包括在脚注中。在收录的论文中有大量的交叉参考;遗憾的是，这些参考文献引用的是按原始页码出现在合集中的其他论文。此外，当对文本的更改影响到注释的编号时，对个别论文内部脚注的交叉引用似乎并不总是得到更新。正文装订得很好，排版紧凑的话很吸引人，而且相对来说没有印刷错误。令人高兴的是，存在的问题很容易纠正。Brian van den Broek曼尼托巴大学哲学系，温尼伯，曼尼托巴，r3t2m8，加拿大。broek@cc.umanitoba.ca。
{"title":"Ian Chiswell and Wilfrid Hodges. Mathematical logic. Oxford Texts in Logic, vol. 3. Oxford University Press, Oxford, England, 2007, 250 pp.","authors":"Robert S. Lubarsky","doi":"10.1017/S1079898600001748","DOIUrl":"https://doi.org/10.1017/S1079898600001748","url":null,"abstract":"that expressions like ‘brother’ and ‘male sibling’ may be translated into the same expression of another language that has only one phrase for the concept while preserving sense. Salmon proposses to resolve the conflict by abandoning Church’s solution to the paradox, noting that doing so appears to undermine the original impetus behind Frege’s distinction between Sinn and Bedeutung. The very possibility of language also discusses Church’s Translation Argument, arguing that the moral of that argument shows that Dummett’s account of language collapses into the absurd position that it is impossible for us to know a language. The volume contain a helpful bibliography of Salmon’s writings from1979–2005. Unfortunately, there is no bibliography of the works cited; the details are included only in footnotes. There is a good deal of cross-referencing amongst the included papers; regrettably, these references refer to other papers that appear in the collection by their original pagination. Furthermore, cross-references to footnotes internal to an individual paper seem not always to have been updated when changes to the text affected the numbering of the notes. The text is well bound, attractively if densely type-set, and relatively free from typographical errors. Happily, those that exist are easily rectified. Brian van den Broek Department of Philosophy, University of Manitoba, Winnipeg, Manitoba, R3T 2M8, Canada. broek@cc.umanitoba.ca.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"265 - 267"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001748","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57302896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-06-01DOI: 10.1017/S1079898600001773
A. Urquhart
Finally, the sentence “The notion of proof net is not decidable in an elementary way” (p. 131) is plain wrong. A proof net consists of a sequence of formulas, equipped with the axiom links (i.e., the coherence graph). The question whether such an object is correct, (i.e., represents an actual proof) can be decided in linear time. Lutz Strassburger École Polytechnique, LIX, Rue de Saclay, 91128 Palaiseau Cedex, France Lutz.Strassburger@inria.fr.
最后，“证明网的概念不能以基本方式确定”(第131页)这句话显然是错误的。证明网由一系列公式组成，并配有公理链(即相干图)。这样一个对象是否正确(即是否代表一个实际证明)的问题可以在线性时间内确定。Lutz Strassburger École巴黎综合理工学院，Rue de Saclay, 91128 Palaiseau Cedex，法国Lutz.Strassburger@inria.fr。
{"title":"Current topics in logic and analytic philosophy. edited by Concha Martínez, José L. Falguera and José M. Sagüillo, Colloquium on Logic and Analytic Philosophy at Santiago de Compostela, 2001–2005. Universidade de Santiago de Compostela, 2007, 288 pp.","authors":"A. Urquhart","doi":"10.1017/S1079898600001773","DOIUrl":"https://doi.org/10.1017/S1079898600001773","url":null,"abstract":"Finally, the sentence “The notion of proof net is not decidable in an elementary way” (p. 131) is plain wrong. A proof net consists of a sequence of formulas, equipped with the axiom links (i.e., the coherence graph). The question whether such an object is correct, (i.e., represents an actual proof) can be decided in linear time. Lutz Strassburger École Polytechnique, LIX, Rue de Saclay, 91128 Palaiseau Cedex, France Lutz.Strassburger@inria.fr.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"271 - 272"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001773","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen (Investigations into logical reasoning) that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents have at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio. We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933.
根岑在其博士论文《逻辑推理的研究》(Untersuchungen ber das logische Schliessen)中写道，他只能证明直觉自然演绎的归一化定理，而不能证明经典演绎的归一化定理。为了解决后者，他发展了经典的序列微积分，并证明了一个相应的定理，即著名的切消定理。它的证明是有组织的，因此直觉序列微积分的切消结果是作为一种特殊情况出现的，即序列在右边的连续部分中最多有一个公式。因此，不需要对直觉自然演绎的归一化进行直接证明。在已发表的论文中，这种证明的唯一痕迹是一些可转换性，例如当一个隐含引入之后是一个隐含消除[1934-35,II.5.13]。直到1965年，达格·普拉维茨才找到了正规化的证明。另一个不太为人所知的证据也是在1965年由安德烈斯·拉乔提出的。我们在2005年2月发现了根岑论文的早期手写版本，与上面的标题完全相同，但内容却截然不同:最值得注意的是，它包含了对自然演绎标准体系的规范化的详细证明。手稿位于苏黎世eth的保罗·伯内斯收藏中，批号为Hs. 974: 271。伯内斯一定是在1933年4月因种族法律被逐出Göttingen之前就已经得到了它。
{"title":"Gentzen's Proof of Normalization for Natural Deduction","authors":"Jan von Plato","doi":"10.2178/bsl/1208442829","DOIUrl":"https://doi.org/10.2178/bsl/1208442829","url":null,"abstract":"Abstract Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen (Investigations into logical reasoning) that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents have at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio. We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"240 - 257"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208442829","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-06-01DOI: 10.1017/S107989860000175X
V. Peckhaus
They report the results, which include 0% getting the correct answer, and in the following discussion mention that their results are typical. The second interlude is the Linda problem. Linda is described (in more detail than this) as being socially concerned and left-leaning. Then eight statements (a)–(h) about Linda are listed, and the subject is asked to rank them in order of probability. Six are red herrings. The two of interest are: (f) Linda is a bank teller, and (h) Linda is a bank teller and is active in the feminist movement. Apparently the majority of participants rank (h) as more likely than (f), presumably because it contains some information more consistent with the overall image of Linda, even though (h) implies (f) whereas (f) does not imply (h). (The authors report that these two phenomena and variants have been intensely studied by psychologists. In fact, one of the researchers behind the latter test, Kahneman, was awarded the Nobel Memorial Prize in Economic Sciences in 2002 for this work, done with Tversky, who had by then passed away.) Another charm of the book are the many photographs of (or, if that is not possible, graphics related to) important figures in logic, with a snippet about their contribution to the field. In fact, the first chapter is just two pages devoted to five mathematicians from Euclid to Gentzen addressing the question as to what mathematics is (as well as a one-page pronunciation guide). Along the way we also meet de Morgan, Łukasiewicz, Hilbert, Peirce, Post, Hintikka, Bolzano, and others. When deciding whether to use this for your course, beside the considerations already mentioned, another along which this fares favorably is price. At $59, it is a chunk cheaper than Mendelson ($85) and Enderton ($102), even if the former is paperback and the latter two hardcover. With the authors’ teaching experience behind them, their offering is well worth considering for your introductory, undergraduate logic course. Robert Lubarsky Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA. Robert.Lubarsky@alum.mit.edu.
他们报告了结果，其中0%的人得到了正确的答案，并在接下来的讨论中提到他们的结果是典型的。第二个插曲是琳达的问题。琳达被描述为(比这更详细)关心社会和左倾。然后列出8个关于Linda的陈述(a) - (h)，并要求被试按概率对它们进行排序。六个是转移注意力。我们感兴趣的两件事是:(f)琳达是一名银行出纳，(h)琳达是一名积极参与女权运动的银行出纳。显然，大多数参与者认为(h)比(f)更有可能，大概是因为它包含了一些与琳达整体形象更一致的信息，尽管(h)暗示了(f)，而(f)并不暗示(h)。(作者报告说，心理学家对这两种现象和变体进行了深入研究。)事实上，后一项测试的研究人员之一卡尼曼(Kahneman)曾因此项研究获得2002年的诺贝尔经济学奖(Nobel Memorial Prize In Economic Sciences)，当时他与特沃斯基(Tversky)共同完成了这项研究，特沃斯基当时已经去世。)这本书的另一个魅力在于许多逻辑学重要人物的照片(或者，如果不可能的话，与之相关的图形)，以及他们对该领域的贡献。事实上，第一章只有两页，专门讨论了从欧几里得到根岑的五位数学家关于数学是什么的问题(以及一页的发音指南)。一路上，我们还会见了德·摩根、Łukasiewicz、希尔伯特、皮尔斯、波斯特、欣蒂卡、博尔扎诺等人。当决定是否在你的课程中使用它时，除了已经提到的考虑之外，另一个有利的因素是价格。59美元的价格比门德尔松(85美元)和恩德顿(102美元)便宜很多，即使前者是平装本，后者是精装本。由于作者的教学经验，他们的作品非常值得你在本科逻辑入门课程中考虑。Robert Lubarsky佛罗里达大西洋大学数学科学系，美国佛罗里达州博卡拉顿33431Robert.Lubarsky@alum.mit.edu。
{"title":"Johann Heinrich Lambert. Philosophische Schriften. Vol. VIII: Kleinere philosophische Abhandlungen und Rezensionen. edited by A. Emmel and A. Spree, Georg Olms Verlag, Hildesheim, Zurich and New York 2007, Part 1: xlii + pp. 1–474; Part 2: pp. 475–763.","authors":"V. Peckhaus","doi":"10.1017/S107989860000175X","DOIUrl":"https://doi.org/10.1017/S107989860000175X","url":null,"abstract":"They report the results, which include 0% getting the correct answer, and in the following discussion mention that their results are typical. The second interlude is the Linda problem. Linda is described (in more detail than this) as being socially concerned and left-leaning. Then eight statements (a)–(h) about Linda are listed, and the subject is asked to rank them in order of probability. Six are red herrings. The two of interest are: (f) Linda is a bank teller, and (h) Linda is a bank teller and is active in the feminist movement. Apparently the majority of participants rank (h) as more likely than (f), presumably because it contains some information more consistent with the overall image of Linda, even though (h) implies (f) whereas (f) does not imply (h). (The authors report that these two phenomena and variants have been intensely studied by psychologists. In fact, one of the researchers behind the latter test, Kahneman, was awarded the Nobel Memorial Prize in Economic Sciences in 2002 for this work, done with Tversky, who had by then passed away.) Another charm of the book are the many photographs of (or, if that is not possible, graphics related to) important figures in logic, with a snippet about their contribution to the field. In fact, the first chapter is just two pages devoted to five mathematicians from Euclid to Gentzen addressing the question as to what mathematics is (as well as a one-page pronunciation guide). Along the way we also meet de Morgan, Łukasiewicz, Hilbert, Peirce, Post, Hintikka, Bolzano, and others. When deciding whether to use this for your course, beside the considerations already mentioned, another along which this fares favorably is price. At $59, it is a chunk cheaper than Mendelson ($85) and Enderton ($102), even if the former is paperback and the latter two hardcover. With the authors’ teaching experience behind them, their offering is well worth considering for your introductory, undergraduate logic course. Robert Lubarsky Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA. Robert.Lubarsky@alum.mit.edu.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"267 - 268"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S107989860000175X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups. They can be characterized as subgroups of metric ultraproducts of families of, respectively, unitary groups U(n) and symmetric groups Sn , n ∈ ℕ. Hyperlinear groups come from theory of operator algebras (Connes' Embedding Problem), while sofic groups, introduced by Gromov, are motivated by a problem of symbolic dynamics (Gottschalk's Surjunctivity Conjecture). Open questions are numerous, in particular it is still unknown if every group is hyperlinear and/or sofic.
{"title":"Hyperlinear and Sofic Groups: A Brief Guide","authors":"V. Pestov","doi":"10.2178/bsl/1231081461","DOIUrl":"https://doi.org/10.2178/bsl/1231081461","url":null,"abstract":"Abstract This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups. They can be characterized as subgroups of metric ultraproducts of families of, respectively, unitary groups U(n) and symmetric groups Sn , n ∈ ℕ. Hyperlinear groups come from theory of operator algebras (Connes' Embedding Problem), while sofic groups, introduced by Gromov, are motivated by a problem of symbolic dynamics (Gottschalk's Surjunctivity Conjecture). Open questions are numerous, in particular it is still unknown if every group is hyperlinear and/or sofic.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"449 - 480"},"PeriodicalIF":0.6,"publicationDate":"2008-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081461","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cherlin Gregory and Hrushovski Ehud . Finite structures with few types . Annals of Mathematics Studies. Princeton University Press, 2003, vi + 196 pp.","authors":"Vera Koponen","doi":"10.2178/bsl/1208358847","DOIUrl":"https://doi.org/10.2178/bsl/1208358847","url":null,"abstract":"Gregory Cherlin and Ehud Hrushovski. Finite structures with few types. Annals of Mathematics Studies. Princeton University Press, 2003, vi + 196pp.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"114 - 116"},"PeriodicalIF":0.6,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208358847","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-03-01DOI: 10.1017/S1079898600001864
Thomas Hofweber
type-amalgamation property in the book. The model theoretic analysis also shows that the class of structures which have a smoothly approximable expansion can be characterized as the class of structures which satisfies nine model theoretic properties, a few of which have just been mentioned. Many of the results presented depend on weaker assumptions than smooth approximability, such as א0-categoricity and finite rank. As shown in [Kantor, Liebeck, Macpherson, op. cit.], every smoothly approximable structure M has the following property, called pseudofiniteness: If φ is a sentence which is true in M then φ is true in a finite substructure of M . It follows that the complete theory of a smoothly approximable structure is not finitely axiomatizable. By developing further the method of envelopes and techniques of G. Ahlbrandt and M. Ziegler (used for strongly minimal totally categorical theories) it is shown that the complete theory of any smoothly approximable structure is quasifinitely axiomatizable, meaning that the theory is axiomatized by a finite number of axiom schemes. This extends earlier results about pseudofiniteness and quasifinite axiomatizability for א0-categorical א0-stable theories. In the last chapter, which builds on methods used for quasifinite axiomatizability, decidability problems are considered. For instance, given a language with a finite signature containing only relation symbols and a sentence in this language, it is decidable whether the sentence has a stable homogeneous model. Also, in a language with finite signature, one can decide whether a sentence has a finite model with a given number of 4-types. For some results the classification of finite simple groups is used and a discussion of this is given at the end of the book. The book is technically difficult, proofs are often quite compressed and it expects that the reader is familiar with various notions from model theory and algebra; so the book demands plenty of the reader. An error (the statement of Lemma 2.4.8) is corrected in [G. Cherlin, M. Djordjević, E. Hrushovski, The Journal of Symbolic Logic, vol. 70 (2005), pp. 1359–1364]. Vera Koponen Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden. vera@math.uu.se.
书中的字体合并特性。模型理论分析还表明，具有光滑近似展开式的一类结构可以表征为满足九个模型理论性质的一类结构，其中一些性质刚才已经提到。所提出的许多结果依赖于较弱的假设，而不是光滑近似性，例如零类别和有限秩。如[Kantor, Liebeck, Macpherson，同前]所示，每一个光滑近似结构M都具有以下性质，称为伪有限性:如果φ是一个在M中为真的句子，则φ在M的有限子结构中为真。由此可见，光滑近似结构的完备理论不是有限公理化的。通过进一步发展G. Ahlbrandt和M. Ziegler的包络方法和技术(用于强极小全范畴理论)，证明了任何光滑近似结构的完备理论是准有限公理化的，即该理论是由有限个公理方案公理化的。这扩展了先前关于零-范畴零稳定理论的伪有限性和准有限公理化性的结果。在最后一章中，建立了准有限公理化性的方法，考虑了可决性问题。例如，给定一种只包含关系符号的有限签名语言和该语言中的一个句子，该句子是否具有稳定的齐次模型是可判定的。此外，在具有有限签名的语言中，人们可以决定一个句子是否具有给定数量的4种类型的有限模型。对于某些结果，使用了有限单群的分类，并在本书的最后给出了对此的讨论。这本书在技术上是困难的，证明往往相当压缩，它期望读者熟悉模型理论和代数的各种概念;所以这本书对读者的要求很高。一个错误(引理2.4.8的陈述)在[G]中得到纠正。Cherlin, M. djordjeviki, E. Hrushovski，《符号逻辑学报》，vol. 70 (2005)， pp. 1359-1364。乌普萨拉大学数学系，瑞典乌普萨拉75106号480号。vera@math.uu.se。
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s of invited and contributed talks given in person or by title by members of the Association follow. For the Program Committee Steffen Lempp Abstracts of invited joint ASL–LICS hour lecturess of invited joint ASL–LICS hour lectures MARTIN HYLAND, Combinatorics of proofs. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, DPMMS, CMS, Wilberforce Road, Cambridge CB3 0WB, UK. E-mail: m.hyland@dpmms.cam.ac.uk. Ideally interpretations of proofs should exhibit some essential combinatorial features in an interesting and appealing way. As a case study, one can consider the notion of innocent strategy which is the basis for a game semantical interpretation of proofs and programmes. Some combinatorial content of this notion is sketched in the joint LICS paper accompanying this talk, whose abstract reads as follows. We show how to construct the category of games and innocent strategies from a more primitive category of games. On that category we define a comonad and monad with the former distributing over the latter. Innocent strategies are the maps in the induced two-sided Kleisli category. Thus the problematic composition of innocent strategies reflects the use of the distributive law. The composition of simple strategies, and the combinatorics of pointers used to give the comonad and monad are themselves described in categorical terms. The notions of view and of legal play arise naturally in the explanation of the distributivity. The category-theoretic perspective provides a clear discipline for the necessary combinatorics. There are other instances of a kind of categorical combinatorics of proofs, but in this talk I shall restrict myself to the one instance. COLIN STIRLING, Higher-order matching, games and automata. School of Informatics, University of Edinburgh, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK. E-mail: cps@inf.ed.ac.uk. We describe a particular case wheremethods such asmodel-checking as used in verification are transferred to simply typed lambda calculus. Higher-order matching is the problem given t = u where t, u are terms of simply typed lambda-calculus and u is closed, is there a substitution S such that tS and u have the same normal formwith respect to beta eta-equality: can t be pattern matched to u? In the talk we consider the question: can we characterize the set of all solution terms to a matching problem? We provide an automata-theoretic account that is relative to resource: given a matching problem and a finite set of variables and constants, the (possibly infinite) set of terms that are built from those components and that solve the problem is regular. The characterization uses standard bottom-up tree automata. However, the technical proof uses a game-theoretic characterization of matching. LOGIC COLLOQUIUM ’07 125 Abstracts of invited joint ASL–LICS thirty-minute lecturess of invited joint ASL–LICS thirty-minute lectures CRISTIANO CALCAGNO, Can logic tame systems programs? Dept. o
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