Search results for 'Mathematics Foundations' (try it on Scholar)

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  1. O. Bradley Bassler (2005). Book Review: J. P. Mayberry. Foundations of Mathematics in the Theory of Sets. [REVIEW] Notre Dame Journal of Formal Logic 46 (1):107-125.score: 180.0
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  2. William Bragg Ewald (ed.) (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford University Press.score: 180.0
    This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated (...)
     
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  3. Hans D. Sluga (ed.) (1993). Logic and Foundations of Mathematics in Frege's Philosophy. Garland Pub..score: 180.0
  4. Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.score: 156.0
    THE FOUNDATIONS OF MATHEMATICS () PREFACE The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with ...
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  5. G. T. Kneebone (1963/2001). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover.score: 156.0
    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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  6. M. Giaquinto (2002). The Search for Certainty: A Philosophical Account of Foundations of Mathematics. Oxford University Press.score: 156.0
    Marcus Giaquinto tells the compelling story of one of the great intellectual adventures of the modern era: the attempt to find firm foundations for mathematics. From the late nineteenth century to the present day, this project has stimulated some of the most original and influential work in logic and philosophy.
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  7. Eric Livingston (1986). The Ethnomethodological Foundations of Mathematics. Routledge & K. Paul.score: 156.0
    A Non-Technical Introduction to Ethnomethodological Investigations of the Foundations of Mathematics through the Use of a Theorem of Euclidean Geometry* I ...
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  8. Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.score: 156.0
    Machine generated contents note: Part I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletabilty theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! (...)
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  9. Laura Crosilla & Peter Schuster (eds.) (2005). From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics. Oxford University Press.score: 156.0
    This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developments, which have been most useful for computer science (ie: constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logician, mathematicians, philosophers and computer scientists with contributions from leading researchers, it is up to date, highly topical and broad in scope.
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  10. Abraham Adolf Fraenkel & Yehoshua Bar-Hillel (eds.) (1966). Essays on the Foundations of Mathematics. Jerusalem, Magnes Press Hebrew University.score: 156.0
    Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...)
     
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  11. Paolo Mancosu (ed.) (1998). From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press.score: 156.0
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these (...)
     
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  12. P. Cariani (2012). Infinity and the Observer: Radical Constructivism and the Foundations of Mathematics. Constructivist Foundations 7 (2):116-125.score: 152.0
    Problem: There is currently a great deal of mysticism, uncritical hype, and blind adulation of imaginary mathematical and physical entities in popular culture. We seek to explore what a radical constructivist perspective on mathematical entities might entail, and to draw out the implications of this perspective for how we think about the nature of mathematical entities. Method: Conceptual analysis. Results: If we want to avoid the introduction of entities that are ill-defined and inaccessible to verification, then formal systems need to (...)
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  13. Frank Waaldijk (2005). On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10 (3):249-324.score: 150.0
    We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely (...)
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  14. Charles Parsons (1967). Mathematics, Foundations Of. In Paul Edwards (ed.), The Encyclopedia of Philosophy. New York, Macmillan. 5--188.score: 150.0
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  15. Ian Stewart & David Tall (1977). The Foundations of Mathematics. Oxford University Press.score: 148.0
    The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.
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  16. Frode Kjosavik (2009). Kant on Geometrical Intuition and the Foundations of Mathematics. Kant-Studien 100 (1):1-27.score: 144.0
    It is argued that geometrical intuition, as conceived in Kant, is still crucial to the epistemological foundations of mathematics. For this purpose, I have chosen to target one of the most sympathetic interpreters of Kant's philosophy of mathematics – Michael Friedman – because he has formulated the possible historical limitations of Kant's views most sharply. I claim that there are important insights in Kant's theory that have survived the developments of modern mathematics, and thus, that they (...)
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  17. Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.score: 144.0
    The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It (...)
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  18. John Bell, The Axiom of Choice in the Foundations of Mathematics.score: 144.0
    The principle of set theory known as the Axiom of Choice (AC) has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago”1 It has been employed in countless mathematical papers, a number of monographs have been exclusively devoted to it, and it has long played a prominently role in discussions on the (...) of mathematics. (shrink)
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  19. Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.score: 144.0
    One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for (...)
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  20. Solomon Feferman, The Development of Programs for the Foundations of Mathematics in the First Third of the 20th Century.score: 144.0
    The most prominent “schools” or programs for the foundations of mathematics that took shape in the first third of the 20th century emerged directly from, or in response to, developments in mathematics and logic in the latter part of the 19th century. The first of these programs, so-called logicism, had as its aim the reduction of mathematics to purely logical principles. In order to understand properly its achievements and resulting problems, it is necessary to review the (...)
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  21. Alex A. B. Aspeitia, Internalism and Externalism in the Foundations of Mathematics.score: 144.0
    Without a doubt, one of the main reasons Platonsim remains such a strong contender in the Foundations of Mathematics debate is because of the prima facie plausibility of the claim that objectivity needs objects. It seems like nothing else but the existence of external referents for the terms of our mathematical theories and calculations can guarantee the objectivity of our mathematical knowledge. The reason why Frege – and most Platonists ever since – could not adhere to the idea (...)
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  22. I. Grattan-Guinness (1982). Psychology in the Foundations of Logic and Mathematics: The Cases of Boole, Cantor and Brouwer. History and Philosophy of Logic 3 (1):33-53.score: 144.0
    In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.
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  23. Paolo Mancosu (1999). Between Russell and Hilbert: Behmann on the Foundations of Mathematics. Bulletin of Symbolic Logic 5 (3):303-330.score: 144.0
    After giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition (...)
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  24. J. P. Mayberry (2000). The Foundations of Mathematics in the Theory of Sets. Cambridge University Press.score: 144.0
    This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
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  25. Vito F. Sinisi (1983). Leśniewski's Foundations of Mathematics. Topoi 2 (1):3-52.score: 144.0
    During 1927-1931 Leśniewski published a series of articles (169 pages) entitled 'O podstawach matematyki' [On the Foundations of Mathematics] in the journal Przeglad Filozoficzny [Philosophical Review], and an abridged English translation of this series is presented here. With the exception of this work, all of Leśniewski's publications appearing after the first World War were written in German, and hence accessible to scholars and logicians in the West. This work, however, since written in Polish, has heretofore not been accessible (...)
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  26. Miriam Franchella (1994). Heyting's Contribution to the Change in Research Into the Foundations of Mathematics. History and Philosophy of Logic 15 (2):149-172.score: 144.0
    After the 1930s, the research into the foundations of mathematics changed.None of its main directions (logicism, formalism and intuitionism) had any longer the pretension to be the only true mathematics.Usually, the determining factor in the change is considered to be Gödel?s work, while Heyting?s role is neglected.In contrast, in this paper I first describe how Heyting directly suggested the abandonment of the big foundational questions and the putting forward of a new kind of foundational research consisting in (...)
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  27. Elena Anne Marchisotto (1995). In the Shadow of Giants: The Work of Mario Pieri in the Foundations of Mathematics. History and Philosophy of Logic 16 (1):107-119.score: 144.0
    (1995). In the shadow of giants: The work of mario pieri in the foundations of mathematics. History and Philosophy of Logic: Vol. 16, No. 1, pp. 107-119.
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  28. William Bragg Ewald (2005). From Kant to Hilbert Volume 1: A Source Book in the Foundations of Mathematics. OUP Oxford.score: 144.0
    Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number theory, analysis, logic and set theory--with (...)
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  29. Colin Mclarty (2013). Foundations as Truths Which Organize Mathematics. Review of Symbolic Logic 6 (1):76-86.score: 144.0
    The article looks briefly at Fefermans own foundations. Among many different senses of foundations, the one that mathematics needs in practice is a recognized body of truths adequate to organize definitions and proofs. Finding concise principles of this kind has been a huge achievement by mathematicians and logicians. We put ZFC and categorical foundations both into this context.
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  30. Crispin Wright (1980). Wittgenstein on the Foundations of Mathematics. Harvard University Press.score: 144.0
  31. Mathieu Marion (1998). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press.score: 138.0
    This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations.
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  32. Peter Verdée (2013). Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics. Foundations of Science 18 (4):655-680.score: 138.0
    In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, also the (...)
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  33. Raymond Louis Wilder (1965/2012). Introduction to the Foundations of Mathematics: Second Edition. Dover Publications, Inc..score: 138.0
    This_classic undergraduate text_elegantly acquaints students with the_fundamental concepts and methods of mathematics. In addition to introducing_many noteworthy historical figures_from the 18th through the mid-20th centuries, it examines_the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, groups, intuitionism,_formal systems, mathematical logic, and other topics.
     
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  34. Moritz Pasch (2010). Essays on the Foundations of Mathematics. Springer.score: 138.0
    Translator's introduction -- Fundamental questions of geometry -- The decidability requirement -- The origin of the concept of number -- Implicit definition and the proper grounding of mathematics -- Rigid bodies in geometry -- Prelude to geometry : the essential ideas -- Physical and mathematical geometry -- Natural geometry -- The concept of the differential -- Reflections on the proper grounding of mathematics I -- Concepts and proofs in mathematics -- Dimension and space in mathematics -- (...)
     
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  35. Ludwig Wittgenstein (1975/1989). Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939: From the Notes of R.G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. University of Chicago Press.score: 132.0
    From his return to Cambridge in 1929 to his death in 1951, Wittgenstein influenced philosophy almost exclusively through teaching and discussion. These lecture notes indicate what he considered to be salient features of his thinking in this period of his life.
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  36. Uri Nodelman & Edward N. Zalta (2014). Foundations for Mathematical Structuralism. Mind 123 (489):39-78.score: 132.0
    We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions (...)
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  37. Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.score: 132.0
    Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is (...)
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  38. Jouko Vaananen (2001). Second-Order Logic and Foundations of Mathematics. Bulletin of Symbolic Logic 7 (4):504-520.score: 132.0
    We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second-order logic are not (...)
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  39. Geoffrey Hellman (2006). Pluralism and the Foundations of Mathematics. In ¸ Itekellersetal:Sp. 65--79.score: 132.0
    A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, (...)
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  40. Juliette Kennedy & Roman Kossak (eds.) (2012). Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies. Cambridge University Press.score: 132.0
    Machine generated contents note: 1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture W. Hugh Woodin; 4. [omega]-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts James H. (...)
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  41. Solomon Feferman (1992). Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455.score: 132.0
    Does science justify any part of mathematics and, if so, what part? These questions are related to the so-called indispensability arguments propounded, among others, by Quine and Putnam; moreover, both were led to accept significant portions of set theory on that basis. However, set theory rests on a strong form of Platonic realism which has been variously criticized as a foundation of mathematics and is at odds with scientific realism. Recent logical results show that it is possible to (...)
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  42. Thomas E. Uebel (2005). Learning Logical Tolerance: Hans Hahn on the Foundations of Mathematics. History and Philosophy of Logic 26 (3):175-209.score: 132.0
    Hans Hahn's long-neglected philosophy of mathematics is reconstructed here with an eye to his anticipation of the doctrine of logical pluralism. After establishing that Hahn pioneered a post-Tractarian conception of tautologies and attempted to overcome the traditional foundational dispute in mathematics, Hahn's and Carnap's work is briefly compared with Karl Menger's, and several significant agreements or differences between Hahn's and Carnap's work are specified and discussed.
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  43. Ludwig Wittgenstein (1978). Remarks on the Foundations of Mathematics. B. Blackwell.score: 132.0
  44. Evert Willem Beth (1959). The Foundations of Mathematics. Amsterdam, North-Holland Pub. Co..score: 132.0
     
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  45. Howard Whitley Eves (1965). An Introduction to the Foundations and Fundamental Concepts of Mathematics. New York, Holt, Rinehart and Winston.score: 132.0
     
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  46. Kurt Gödel, Jack J. Bulloff, Thomas C. Holyoke & Samuel Wilfred Hahn (eds.) (1969). Foundations of Mathematics. New York, Springer.score: 132.0
     
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  47. R. L. Goodstein (1951). The Foundations of Mathematics: An Inaugural Lecture Delivered at the University College of Leicester, 13th November 1951. University College.score: 132.0
  48. William S. Hatcher (1968). Foundations of Mathematics. Philadelphia, W. B. Saunders Co..score: 132.0
  49. William S. Hatcher (1982). The Logical Foundations of Mathematics. Pergamon Press.score: 132.0
  50. Stephen Cole Kleene (1965). The Foundations of Intuitionistic Mathematics. Amsterdam, North-Holland Pub. Co..score: 132.0
     
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