Search results for 'Logic, Symbolic and mathematical Study and teaching' (try it on Scholar)

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  1.  17
    Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.) (2009). Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge.
    Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help ...
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  2. Zoltan P. Dienes (1966). Learning Logic, Logical Games. [New York]Herder and Herder.
     
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  3.  53
    Xinli Wang (2009). Symbolic Logic Study Guide (a Textbook). University Readers.
    The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve sample (...)
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  4. Andrzej Mostowski (1966). Thirty Years of Foundational Studies Lectures on the Development of Mathematical Logic and the Study of the Foundations of Mathematics in 1930-1964. Blackwell.
     
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  5. Maurice Joseph Burke (ed.) (2008). Navigating Through Reasoning and Proof in Grades 9-12. National Council of Teachers of Mathematics.
     
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  6. John Corcoran, LOGIC TEACHING IN THE 21ST CENTURY.
    We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, (...)
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  7.  13
    J. L. Bell (1977). A Course in Mathematical Logic. Sole Distributors for the U.S.A. And Canada American Elsevier Pub. Co..
    A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.
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  8.  54
    Stephen Cole Kleene (1967). Mathematical Logic. Dover Publications.
    Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part (...)
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  9.  22
    Ian Chiswell (2007). Mathematical Logic. Oxford University Press.
    Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of (...)
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  10. Abraham Robinson (1968). Mostowski Andrzej. Thirty Years of Foundational Studies. Lectures on the Development of Mathematical Logic and the Study of the Foundations of Mathematics in 1930–1964. Acta Philosophica Fennica, No. 17, Helsinki 1965, and Barnes & Noble, Inc., New York 1966, 180 Pp.; Second Printing, Helsinki 1967, 180 Pp. [REVIEW] Journal of Symbolic Logic 33 (1):111-112.
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  11.  21
    Heinz-Dieter Ebbinghaus (1996). Mathematical Logic. Springer.
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The (...)
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  12. Ann M. Singleterry (1967). Review: Patrick Suppes, Mathematical Logic for the Schools; Patrick Suppes, Frederick Binford, Experimental Teaching of Mathematical Logic in the Elementary School. [REVIEW] Journal of Symbolic Logic 32 (3):422-422.
     
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  13. Eberhard Herrmann & Rodney Downey (1990). Soare Robert I.. Recursively Enumerable Sets and Degrees. A Study of Computable Functions and Computably Generated Sets. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, Heidelberg, New York, Etc., 1987, Xviii + 437 Pp. [REVIEW] Journal of Symbolic Logic 55 (1):356-357.
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  14. Carlos Augusto Di Prisco (1986). Solovay Robert M., Reinhardt William N., and Kanamori Akihiro. Strong Axioms of Infinity and Elementary Embeddings. Annals of Mathematical Logic, Vol. 13 , Pp. 73–116.Magidor Menachem. HOW Large is the First Strongly Compact Cardinal? Or A Study on Identity Crises. Annals of Mathematical Logic, Vol. 10 , Pp. 33–57. [REVIEW] Journal of Symbolic Logic 51 (4):1066-1068.
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  15. Ann M. Singleterry (1967). Suppes Patrick. Mathematical Logic for the Schools. The Arithmetic Teacher, Vol. 9 , Pp. 396–399.Suppes Patrick and Binford Frederick. Experimental Teaching of Mathematical Logic in the Elementary School. The Arithmetic Teacher, Vol. 12 , Pp. 187–195. [REVIEW] Journal of Symbolic Logic 32 (3):422.
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  16. Graeme Forbes (1994). Modern Logic: A Text in Elementary Symbolic Logic. Oxford University Press.
    Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a special appendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, (...)
     
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  17.  48
    G. T. Kneebone (1963). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover.
    Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.
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  18.  15
    M. Ben-Ari (1993). Mathematical Logic for Computer Science. Prentice Hall.
    Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.The logical systems presented are:- Propositional calculus (including binary decision diagrams);- Predicate calculus;- Resolution;- Hoare logic;- (...)
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  19. Walter Carnielli (1986). Seventh Latin American on Mathematical Logic- Meeting of the Association for Symbolic Logic: Campinas, Brazil, 1985. Journal of Symbolic Logic 51 (4):1093-1103.
    This publication refers to the proceedings of the Seventh Latin American on Mathematical Logic held in Campinas, SP, Brazil, from July 29 to August 2, 1985. The event, dedicated to the memory of Ayda I. Arruda, was sponsored as an official Meeting of the Association for Symbolic Logic. Walter Carnielli. -/- The Journal of Symbolic Logic Vol. 51, No. 4 (Dec., 1986), pp. 1093-1103.
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  20.  11
    Rudolf Carnap (1988). Meaning and Necessity: A Study in Semantics and Modal Logic. University of Chicago Press.
    This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).
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  21. B. Othanel Smith & Milton Otto Meux (1970). A Study of the Logic of Teaching.
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  22.  6
    Johanna N. Y. Franklin (forthcoming). Reviewed Work(S): Lowness Properties and Randomness. Advances in Mathematics, Vol. 197 by André Nies; Lowness for the Class of Schnorr Random Reals. SIAM Journal on Computing, Vol. 35 by Bjørn Kjos-Hanssen; André Nies; Frank Stephan; Lowness for Kurtz Randomness. The Journal of Symbolic Logic, Vol. 74 by Noam Greenberg; Joseph S. Miller; Randomness and Lowness Notions Via Open Covers. Annals of Pure and Applied Logic, Vol. 163 by Laurent Bienvenu; Joseph S. Miller; Relativizations of Randomness and Genericity Notions. The Bulletin of the London Mathematical Society, Vol. 43 by Johanna N. Y. Franklin; Frank Stephan; Liang Yu; Randomness Notions and Partial Relativization. Israel Journal of Mathematics, Vol. 191 by George Barmpalias; Joseph S. Miller; André Nies. [REVIEW] Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.
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  23.  11
    Robert Brandom & N. Rescher (1979). The Logic of Inconsistency: A Study in Nonstandard Possible-World Semantics and Ontology. American Philosophical Quarterly, Library of Philosophy 5 (1):233-236.
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  24. Imre Lakatos (ed.) (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or (...)
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  25. Nino Cocchiarella (1974). Tense Logic a Study of Temporal Reference. University Microfilms International.
     
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  26.  10
    Aleksy Mołczanow (2012). Quantification: Transcending Beyond Frege's Boundaries: A Case Study in Transcendental-Metaphysical Logic. Brill.
    Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely ...
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  27.  6
    John R. Gregg (1956). The Language of Taxonomy. An Application of Symbolic Logic to the Study of Classificatory Systems. Journal of Symbolic Logic 21 (4):396-397.
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  28.  1
    Carl G. Hempel (1956). Review: John R. Gregg, The Language of Taxonomy. An Application of Symbolic Logic to the Study of Classificatory Systems. [REVIEW] Journal of Symbolic Logic 21 (4):396-397.
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  29. Carl G. Hempel (1956). Gregg John R.. The Language of Taxonomy. An Application of Symbolic Logic to the Study of Classificatory Systems. Columbia University Press, New York 1954, Ix + 70 Pp. [REVIEW] Journal of Symbolic Logic 21 (4):396-397.
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  30.  19
    Herbert B. Enderton (1972). A Mathematical Introduction to Logic. New York,Academic Press.
    A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, (...)
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  31.  9
    Volker Peckhaus (2009). The Mathematical Origins of Nineteenth-Century Algebra of Logic. In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press 159.
    This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical context will be dealt with only in passing. The main object of study will be the algebra of logic in its British and German versions. Special emphasis will be laid on the systems of George Boole and above all of his German follower Ernst Schröder.
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  32.  3
    Itaï Ben Yaacov (2015). Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras I: Stability. Bulletin of the London Mathematical Society, Vol. 45 , No. 4, Pp. 825–838, Doi:10.1112/Blms/Bdt014.Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras II: Model Theory. Israel Journal of Mathematics, Vol. 201 , No. 1, Pp. 477–505, Doi:10.1007/S11856-014-1046-7.Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras III: Elementary Equivalence and II1 Factors. Bulletin of the London Mathematical Society, Vol. 46 , No. 3, Pp. 609–628, Doi:10.1112/Blms/Bdu012.Isaac Goldbring, Bradd Hart, and Thomas Sinclair. The Theory of Tracial von Neumann Algebras Does Not Have a Model Companion. Journal of Symbolic Logic, Vol. 78 , No. 3, Pp. 1000–1004. [REVIEW] Bulletin of Symbolic Logic 21 (4):425-427.
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  33.  6
    Review by: James Cummings (2015). Reviewed Work: Recent Papers on the Tree Property. Aronszajn Trees and Failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic, Vol. 9, No. 1 , The Tree Property at ℵ Ω+1. Journal of Symbolic Logic, Vol. 77, No. 1 , The Tree Property and the Failure of SCH at Uncountable Confinality. Archive for Mathematical Logic, Vol. 51, No. 5-6 , The Tree Property and the Failure of the Singular Cardinal Hypothesis at [Image]. Journal of Symbolic Logic, Vol. 77, No. 3 , Aronszajn Trees and the Successors of a Singular Cardinal. Archive for Mathematical Logic, Vol. 52, No. 5-6 , The Tree Property Up to ℵ Ω+1. Journal of Symbolic Logic. Vol. 79, No. 2 by Itay Neeman; Dima Sinapova; Spencer Unger. [REVIEW] Bulletin of Symbolic Logic 21 (2):188-192.
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  34.  2
    Burt C. Hopkins (2011). The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein. Indiana University Press.
    Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts (...)
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  35.  2
    Toshiyasu Arai (2002). Buchholz Wilfried. Notation Systems for Infinitary Derivations. Archive for Mathematical Logic, Vol. 30 No. 5–6 , Pp. 277–296.Buchholz Wilfried. Explaining Gentzen's Consistency Proof Within Infinitary Proof Theory. Computational Logic and Proof Theory, 5th Kurt Gödel Colloquium, KGC '97, Vienna, Austria, August 25–29, 1997, Proceedings, Edited by Gottlob Georg, Leitsch Alexander, and Mundici Daniele, Lecture Notes in Computer Science, Vol. 1289, Springer, Berlin, Heidelberg, New York, Etc., 1997, Pp. 4–17.Tupailo Sergei. Finitary Reductions for Local Predicativity, I: Recursively Regular Ordinals. Logic Colloquium '98, Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Prague, Czech Republic, August 9–15, 1998, Edited by Buss Samuel R., Háajek Petr, and Pudlák Pavel, Lecture Notes in Logic, No. 13, Association for Symbolic Logic, Urbana, and A K Peters, Natick, Mass., Etc., 2000, Pp. 465–499. [REVIEW] Bulletin of Symbolic Logic 8 (3):437-439.
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  36.  2
    Andrea Cantini (2002). Sets and Proofs, Invited Papers From Logic Colloquium '97—European Meeting of the Association for Symbolic Logic, Leeds, July 1997. Thomas Strahm. First Steps Into Metapredicativity in Explicit Mathematics. Sets and Proofs, Invited Papers From Logic Colloquium '97—European Meeting of the Association for Symbolic Logic, Leeds, July 1997, Edited by S. Barry Cooper and John K. Truss, London Mathematical Society Lecture Note Series, No. 258, Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1999, Pp. 383–402. [REVIEW] Bulletin of Symbolic Logic 8 (4):535-536.
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  37.  5
    Robert McNaughton (1997). Robinson Raphael M.. Restricted Set-Theoretical Definitions in Arithmetic. Proceedings of the American Mathematical Society, Vol. 9 (1958), Pp. 238–242. Robinson Raphael M.. Restricted Set-Theoretical Definitions in Arithmetic. Summaries of Talks Presented at the Summer Institute for Symbolic Logic, Cornell University, 1957, 2nd Edn., Communications Research Division, Institute for Defense Analyses, Princeton, NJ, 1960, Pp. 139–140. [REVIEW] Journal of Symbolic Logic 31 (4):659-660.
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  38.  9
    James W. Cummings (2000). Apter Arthur W.. On the Least Strongly Compact Cardinal. Israel Journal of Mathematics, Vol. 35 (1980), Pp. 225–233. Apter Arthur W.. Measurability and Degrees of Strong Compactness. The Journal of Symbolic Logic, Vol. 46 (1981), Pp. 249–254. Apter Arthur W.. A Note on Strong Compactness and Supercompactness. Bulletin of the London Mathematical Society, Vol. 23 (1991), Pp. 113–115. Apter Arthur W.. On the First N Strongly Compact Cardinals. Proceedings of the American Mathematical Society, Vol. 123 ... [REVIEW] Bulletin of Symbolic Logic 6 (1):86-89.
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  39.  5
    Andrea Cantini (2002). Strahm Thomas. First Steps Into Metapredicativity in Explicit Mathematics. Sets and Proofs, Invited Papers From Logic Colloquium'97—European Meeting of the Association for Symbolic Logic, Leeds, July 1997, Edited by Cooper S. Barry and Truss John K., London Mathematical Society Lecture Note Series, No. 258, Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1999, Pp. 383–402. [REVIEW] Bulletin of Symbolic Logic 8 (4):535-536.
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  40.  3
    Fernando Ferreira (2002). Strahm Thomas. Polynomial Time Operations in Explicit Mathematics. The Journal of Symbolic Logic, Vol. 62 (1997), Pp. 575–594. Cantini Andrea. Feasible Operations and Applicative Theories Based on Λη. Mathematical Logic Quarterly, Vol. 46 (2000), Pp. 291–312. [REVIEW] Bulletin of Symbolic Logic 8 (4):534-535.
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  41.  1
    James W. Cummings (2000). Apter Arthur W.. On the Least Strongly Compact Cardinal. Israel Journal of Mathematics, Vol. 35 , Pp. 225–233.Apter Arthur W.. Measurability and Degrees of Strong Compactness. The Journal of Symbolic Logic, Vol. 46 , Pp. 249–254.Apter Arthur W.. A Note on Strong Compactness and Supercompactness. Bulletin of the London Mathematical Society, Vol. 23 , Pp. 113–115.Apter Arthur W.. On the First N Strongly Compact Cardinals. Proceedings of the American Mathematical Society, Vol. 123 , Pp. 2229–2235.Apter Arthur W. And Shelah Saharon. On the Strong Equality Between Supercompactness and Strong Compactness.. Transactions of the American Mathematical Society, Vol. 349 , Pp. 103–128.Apter Arthur W. And Shelah Saharon. Menas' Result is Best Possible. Ibid., Pp. 2007–2034.Apter Arthur W.. More on the Least Strongly Compact Cardinal. Mathematical Logic Quarterly, Vol. 43 , Pp. 427–430.Apter Arthur W.. Laver Indestructibility and the Class of Compact Cardinals. The Journal of Symbolic Logic, Vol. 63. [REVIEW] Bulletin of Symbolic Logic 6 (1):86-89.
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  42.  1
    Randall R. Dipert (1992). Shearman A. T.. The Development of Symbolic Logic. A Critical-Historical Study of the Logical Calculus. A Reprint of 1413. Thoemmes, Bristol 1990, Xi + 242 Pp. [REVIEW] Journal of Symbolic Logic 57 (4):1485-1487.
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  43.  1
    H. E. Vaughan (1953). Robinson Abraham. On the Application of Symbolic Logic to Algebra. Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30-September 6, 1950, American Mathematical Society, Providence 1952, Vol. I, Pp. 686–694.Tarski Alfred. Some Notions and Methods on the Borderline of Algebra and Metamathematics. Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30-September 6, 1950, American Mathematical Society, Providence 1952, Vol. I, Pp. 705–720. [REVIEW] Journal of Symbolic Logic 18 (2):182.
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  44.  5
    Howard S. Becker (2002). Jackson Steve. A New Proof of the Strong Partition Relation on Ω1. Transactions of the American Mathematical Society, Vol. 320 (1990), Pp. 737–745. Jackson Steve. Admissible Suslin Cardinals in L (R). The Journal of Symbolic Logic, Vol. 56 (1991), Pp. 260–275. Jackson Steve. A Computation Of. Memoirs of the American Mathematical Society, No. 670. American Mathematical Society, Providence 1999, Viii+ 94 Pp. [REVIEW] Bulletin of Symbolic Logic 8 (4):546-548.
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  45.  9
    G. Sabbagh (1994). Conference on Mathematical Logic: Co-Sponsored by the Association for Symbolic Logic, Pasris, 1992. Journal of Symbolic Logic 59 (1):345.
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  46.  3
    Randall R. Dipert (1992). Review: A. T. Shearman, The Development of Symbolic Logic. A Critical-Historical Study of the Logical Calculus. [REVIEW] Journal of Symbolic Logic 57 (4):1485-1487.
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  47. Arthur W. Apter (2002). Transactions of the American Mathematical Society. James Cummings. A Model in Which GCH Holds at Successors but Fails at Limits. Transactions of the American Mathematical Society, Vol. 329 , Pp. 1–39. James Cummings. Strong Ultrapowers and Long Core Models. The Journal of Symbolic Logic, Vol. 58 , Pp. 240–248. James Cummings. Coherent Sequences Versus Radin Sequences. Annals of Pure and Applied Logic, Vol. 70 , Pp. 223–241. James Cummings, Matthew Foreman, and Menachem Magidor. Squares, Scales and Stationary Reflection. Journal of Mathematical Logic, Vol. 1 , Pp. 35–98. [REVIEW] Bulletin of Symbolic Logic 8 (4):550-552.
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  48. Howard S. Becker (2002). Transactions of the American Mathematical Society. Steve Jackson. A New Proof of the Strong Partition Relation on Ω1. Transactions of the American Mathematical Society, Vol. 320 , Pp. 737–745. Steve Jackson. Admissible Suslin Cardinals in L. The Journal of Symbolic Logic, Vol. 56 , Pp. 260–275. Steve Jackson. A Computation Of. Memoirs of the American Mathematical Society, No. 670. American Mathematical Society, Providence 1999, Viii + 94 Pp. [REVIEW] Bulletin of Symbolic Logic 8 (4):546-548.
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  49. Alonzo Church (1939). Mac Lane Saunders. Symbolic Logic. The American Mathematical Monthly, Vol. 46 , Pp. 289–296. Journal of Symbolic Logic 4 (3):125-126.
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  50. James Cummings (2015). Itay Neeman. Aronszajn Trees and Failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic, Vol. 9, No. 1 , Pp. 139–157.Dima Sinapova. The Tree Property at אּω+1. Journal of Symbolic Logic, Vol. 77, No. 1 , Pp. 279–290.Dima Sinapova. The Tree Property and the Failure of SCH at Uncountable Cofinality. Archive for Mathematical Logic, Vol. 51, No. 5-6 , Pp. 553–562.Dima Sinapova. The Tree Property and the Failure of the Singular Cardinal Hypothesis at אּω 2. Journal of Symbolic Logic, Vol. 77, No. 3 , Pp. 934–946.Spencer Unger. Aronszajn Trees and the Successors of a Singular Cardinal. Archive for Mathematical Logic, Vol. 52, No. 5-6 , Pp. 483–496.Itay Neeman. The Tree Property Up to אּω+1. Journal of Symbolic Logic. Vol. 79, No. 2 , Pp. 429–459. [REVIEW] Bulletin of Symbolic Logic 21 (2):188-192.
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