Search results for 'Mathematical notation' (try it on Scholar)

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  1. William James Meyers (1975). A Mathematical Theory of Parenthesis, Free Notations. Państwowe Wydawn. Naukowe.score: 96.0
     
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  2. W. E. Underwood (forthcoming). Symbolic Configurations and Two-Dimensional Mathematical Notation. Semiotics:523-532.score: 90.0
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  3. W. Douglas Maurer (1999). The Influence of the Computer Upon Mathematical Notation. Semiotica 125 (1-3):165-168.score: 90.0
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  4. Yanjie Zhao (forthcoming). What Is Mathematical Notation: An Interdisciplinary Approach1. Semiotics:257-273.score: 90.0
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  5. Yanjie Zhao (forthcoming). What is Mathematical Notation. Semiotics:257-273.score: 90.0
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  6. Robert Feys (1969). Dictionary of Symbols of Mathematical Logic. Amsterdam, North-Holland Pub. Co..score: 78.0
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  7. Ivor Bulmer-Thomas (1985). Boethian Number Theory Michael Masi: Boethian Number Theory: A Translation of the De Institutione Arithmetica (with Introduction and Notes). (Studies in Classical Antiquity, 6.) Pp. 198; 8 Figures with Mathematical Diagrams and Musical Notation in Text. Amsterdam: Editions Rodopi, 1983. Paper, Fl. 60. [REVIEW] The Classical Review 35 (01):86-87.score: 72.0
  8. Toshiyasu Arai (2002). Buchholz Wilfried. Notation Systems for Infinitary Derivations. Archive for Mathematical Logic, Vol. 30 No. 5–6 (1991), 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 ... [REVIEW] Bulletin of Symbolic Logic 8 (3):437-439.score: 72.0
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  9. Gregory Landini (2012). Frege's Notations: What They Are and How They Mean. Palgrave Macmillan.score: 66.0
     
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  10. Michael Kohlhase, Adaptation of Notations in Living Mathematical Documents.score: 62.0
    Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are fixed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading (...)
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  11. Michael Kohlhase, Notations for Living Mathematical Documents.score: 62.0
    Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are fixed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading (...)
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  12. Madeline M. Muntersbjorn (1999). Naturalism, Notation, and the Metaphysics of Mathematics. Philosophia Mathematica 7 (2):178-199.score: 60.0
    The instability inherent in the historical inventory of mathematical objects challenges philosophers. Naturalism suggests we can construct enduring answers to ontological questions through an investigation of the processes whereby mathematical objects come into existence. Patterns of historical development suggest that mathematical objects undergo an intelligible process of reification in tandem with notational innovation. Investigating changes in mathematical languages is a necessary first step towards a viable ontology. For this reason, scholars should not modernize historical texts without (...)
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  13. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.score: 54.0
    This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive (...) facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)
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  14. Eszter Szabó Attila Krajcsi (2012). The Role of Number Notation: Sign-Value Notation Number Processing is Easier Than Place-Value. Frontiers in Psychology 3.score: 54.0
    Number notations can influence the way numbers are handled in computations; however, the role of notation itself in mental processing has not been examined directly. From a mathematical point of view, it is believed that place-value number notation systems, such as the Indo-Arabic numbers, are superior to sign-value systems, such as the Roman numbers. However, sign-value notation might have sufficient efficiency; for example, sign-value notations were common in flourishing cultures, such as in ancient Egypt. Herein we (...)
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  15. Attila Krajcsi & Eszter Szabó (2012). The Role of Number Notation: Sign-Value Notation Number Processing is Easier Than Place-Value. Frontiers in Psychology 3.score: 54.0
    Number notations can influence the way numbers are handled in computations; however, the role of notation itself in mental processing has not been examined directly. From a mathematical point of view, it is believed that place-value number notation systems, such as the Indo-Arabic numbers, are superior to sign-value systems, such as the Roman numbers. However, sign-value notation might have sufficient efficiency; for example, sign-value notations were common in flourishing cultures, such as in ancient Egypt. Herein we (...)
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  16. Jan Von Plato (2007). In the Shadows of the Löwenheim-Skolem Theorem: Early Combinatorial Analyses of Mathematical Proofs. Bulletin of Symbolic Logic 13 (2):189-225.score: 42.0
    The Löwenheim-Skolem theorem was published in Skolem's long paper of 1920, with the first section dedicated to the theorem. The second section of the paper contains a proof-theoretical analysis of derivations in lattice theory. The main result, otherwise believed to have been established in the late 1980s, was a polynomial-time decision algorithm for these derivations. Skolem did not develop any notation for the representation of derivations, which makes the proofs of his results hard to follow. Such a formal (...) is given here by which these proofs become transparent. A third section of Skolem's paper gives an analysis for derivations in plane projective geometry. To clear a gap in Skolem's result, a new conservativity property is shown for projective geometry, to the effect that a proper use of the axiom that gives the uniqueness of connecting lines and intersection points requires a conclusion with proper cases (logically, a disjunction in a positive part) to be proved. The forgotten parts of Skolem's first paper on the Löwenheim-Skolem theorem are the perhaps earliest combinatorial analyses of formal mathematical proofs, and at least the earliest analyses with profound results. (shrink)
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  17. Stefano Mazzanti (2013). Iteration on Notation and Unary Functions. Mathematical Logic Quarterly 59 (6):415-434.score: 36.0
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  18. James Robert Brown (1999). Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. Routledge.score: 34.0
    Philosophy of Mathematics is clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.
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  19. James Robert Brown (2008). Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures. Routledge.score: 34.0
    1. Introduction : the mathematical image -- 2. Platonism -- 3. Picture-proofs and Platonism -- 4. What is applied mathematics? -- 5. Hilbert and Gödel -- 6. Knots and notation -- 7. What is a definition? -- 8. Constructive approaches -- 9. Proofs, pictures and procedures in Wittgenstein -- 10. Computation, proof and conjecture -- 11. How to refute the continuum hypothesis -- 12. Calling the bluff.
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  20. Axel Gelfert (2011). Mathematical Formalisms in Scientific Practice: From Denotation to Model-Based Representation. Studies in History and Philosophy of Science 42 (2):272-286.score: 30.0
    The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible (...)
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  21. Stephen Cole Kleene (1967/2002). Mathematical Logic. Dover Publications.score: 30.0
    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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  22. Hans Moravec (1995). Roger Penrose's Gravitonic Brains: A Review of Shadows of the Mind by Roger Penrose. [REVIEW] Psyche 2 (1).score: 30.0
    Summarizing a surrounding 200 pages, pages 179 to 190 of Shadows of the Mind contain a future dialog between a human identified as "Albert Imperator" and an advanced robot, the "Mathematically Justified Cybersystem", allegedly Albert's creation. The two have been discussing a Gödel sentence for an algorithm by which a robot society named SMIRC certifies mathematical proofs. The sentence, referred to in mathematical notation as Omega(Q*), is to be precisely constructed from on a definition of SMIRC's algorithm. (...)
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  23. Thomas J. Scheff (2007). A Concept of Social Integration. Philosophical Psychology 20 (5):579 – 593.score: 30.0
    Clear definitions of alienation and solidarity are needed as a step toward an explicit theory of social integration. The idea of alienation has played a key role in the development of sociology, but it's meaning has never been clear. Both theories and empirical studies confound relational-dispositional, cognitive-emotional and/or interpersonal-societal components. This essay proposes definitions that follow from the work of Erving Goffman and others. Goffman's idea of "co-presence" implies a model of solidarity as mutual awareness to the point of merging (...)
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  24. Front Page, Earliest Uses of Symbols of Set Theory and Logic.score: 30.0
    The study of logic goes back more than two thousand years and in that time many symbols and diagrams have been devised. Around 300 BC Aristotle introduced letters as term-variables, a "new and epoch-making device in logical technique." (W. & M. Kneale The Development of Logic (1962, p. 61). The modern era of mathematical notation in logic began with George Boole (1815- 1864), although none of his notation survives. Set theory came into being in the late 19th (...)
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  25. Thomas J. Scheff (2005). The Structure of Context: Deciphering "Frame Analysis". Sociological Theory 23 (4):368-385.score: 30.0
    This article proposes that Goffman's "Frame Analysis" can be interpreted as a step toward unpacking the idea of context. His analysis implies a recursive model involving frames within frames. The key problem is that neither Goffman nor anyone else has clearly defined what is meant by a frame. I propose that it can be represented by a word, phrase, or proposition. A subjective context can be represented as an assembly of these items, joined together by operators such as and, since, (...)
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  26. Pavel Tichy (1986). Constructions. Philosophy of Science 53 (4):514-534.score: 30.0
    The paper deals with the semantics of mathematical notation. In arithmetic, for example, the syntactic shape of a formula represents a particular way of specifying, arriving at, or constructing an arithmetical object (that is, a number, a function, or a truth value). A general definition of this sense of "construction" is proposed and compared with related notions, in particular with Frege's concept of "function" and Carnap's concept of "intensional isomorphism." It is argued that constructions constitute the proper subject (...)
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  27. Chen Chung Chang (1966). Continuous Model Theory. Princeton, Princeton University Press.score: 30.0
    CONTINUOUS MODEL THEORY CHAPTER I TOPOLOGICAL PRELIMINARIES. Notation Throughout the monograph our mathematical notation does not differ drastically from ...
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  28. Fulya Horozal, Florian Rabe & Michael Kohlhase, Extending OpenMath with Sequences.score: 30.0
    Sequences play a great role in mathematical communication. In mathematical notation, we use sequence ellipsis (. . . ) to denote "obvious" sequences like 1, 2, . . . , 7, and in conceptualizations sequence constructors like (i 2+1) i∈N. Furthermore, sequences have a prominent role as argument sequences of flexary functions. While the former cases can adequately be represented and reasoned about as domain objects in Open- Math and MathML, argument sequences are at the language level, (...)
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  29. Vladislav A. Shaposhnikov (1999). Mathematical Notational Systems and the Visual Representation of Metaphysical Ideas. Semiotica 125 (1-3):135-142.score: 30.0
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  30. William M. Farmer & Joshua D. Guttman (2000). A Set Theory with Support for Partial Functions. Studia Logica 66 (1):59-78.score: 28.0
    Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, (...)
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  31. Michael Kohlhase, Cdmtcs.score: 26.0
    In the last two decades, the World Wide Web has become the universal, and — for many users — main information source. Search engines can efficiently serve daily life information needs due to the enormous redundancy of relevant resources on the web. For educational — and even more so for scientific information needs, the web functions much less efficiently: Scientific publishing is built on a culture of unique reference publications, and moreover abounds with specialized structures, such as technical nomenclature, notational (...)
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  32. Steve Awodey (2009). From Sets to Types to Categories to Sets. .score: 24.0
    Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby. In order to stay focused on the “big picture”, we merely sketch the overall form of each construction, referring to (...)
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  33. Letitia Meynell (2008). Why Feynman Diagrams Represent. International Studies in the Philosophy of Science 22 (1):39 – 59.score: 24.0
    There are two distinct interpretations of the role that Feynman diagrams play in physics: (i) they are calculational devices, a type of notation designed to keep track of complicated mathematical expressions; and (ii) they are representational devices, a type of picture. I argue that Feynman diagrams not only have a calculational function but also represent: they are in some sense pictures. I defend my view through addressing two objections and in so doing I offer an account of representation (...)
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  34. Richard Zach (2003). The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program. Synthese 137 (1-2):211 - 259.score: 24.0
    After a brief flirtation with logicism around 1917, David Hilbertproposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays andWilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for everstronger and more comprehensive areas of mathematics, and finitisticproofs of consistency of these systems. Early advances in these areaswere made by Hilbert (and Bernays) in a series of lecture courses atthe (...)
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  35. Peter Woelert (2012). Idealization and External Symbolic Storage: The Epistemic and Technical Dimensions of Theoretic Cognition. Phenomenology and the Cognitive Sciences 11 (3):335-366.score: 24.0
    This paper explores some of the constructive dimensions and specifics of human theoretic cognition, combining perspectives from (Husserlian) genetic phenomenology and distributed cognition approaches. I further consult recent psychological research concerning spatial and numerical cognition. The focus is on the nexus between the theoretic development of abstract, idealized geometrical and mathematical notions of space and the development and effective use of environmental cognitive support systems. In my discussion, I show that the evolution of the theoretic cognition of space apparently (...)
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  36. André Gleyzal (1974). Relative Tensor Calculus and the Tensor Time Derivative. Foundations of Physics 4 (1):23-30.score: 24.0
    A relative tensor calculus is formulated for expressing equations of mathematical physics. A tensor time derivative operator ▽ b a is defined which operates on tensors λia...ib. Equations are written in a rigid, flat, inertial or other coordinate system a, altered to relative tensor notation, and are thereby expressed in general flowing coordinate systems or materials b, c, d, .... Mirror tensor expressions for ▽ b a λic...id and ▽ b a λic...id exist in a relative geometry G (...)
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  37. Raul Hakli & Sara Negri (2011). Reasoning About Collectively Accepted Group Beliefs. Journal of Philosophical Logic 40 (4):531-555.score: 24.0
    A proof-theoretical treatment of collectively accepted group beliefs is presented through a multi-agent sequent system for an axiomatization of the logic of acceptance. The system is based on a labelled sequent calculus for propositional multi-agent epistemic logic with labels that correspond to possible worlds and a notation for internalized accessibility relations between worlds. The system is contraction- and cut-free. Extensions of the basic system are considered, in particular with rules that allow the possibility of operative members or legislators. Completeness (...)
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  38. Yingxu Wang (2003). Using Process Algebra to Describe Human and Software Behaviors. Brain and Mind 4 (2):199-213.score: 24.0
    Although there are various ways to express actions and behaviors in natural languages, it is found in cognitive informatics that human and system behaviors may be classified into three basic categories: to be , to have , and to do . All mathematical means and forms, in general, are an abstract description of these three categories of system behaviors and their common rules. Taking this view, mathematical logic may be perceived as the abstract means for describing to be, (...)
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  39. Authur A. Frost (1975). Matrix Formulation of Special Relativity in Classical Mechanics and Electromagnetic Theory. Foundations of Physics 5 (4):619-641.score: 24.0
    The two-component spinor theory of van der Waerden is put into a convenient matrix notation. The mathematical relations among various types of matrices and the rule for forming covariant expressions are developed. Relativistic equations of classical mechanics and electricity and magnetism are expressed in this notation. In this formulation the distinction between time and space coordinates in the four-dimensional space-time continuum falls out naturally from the assumption that a four-vector is represented by a Hermitian matrix. The indefinite (...)
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  40. M. Randall Holmes, Polymorphic Type Checking for the Type Theory of the Principia Mathematica of Russell and Whitehead.score: 24.0
    This is a brief report on results reported at length in our paper [2], made for the purpose of a presentation at the workshop to be held in November 2011 in Cambridge on the Principia Mathematica of Russell and Whitehead ([?], hereinafter referred to briefly as PM ). That paper grew out of a reading of the paper [3] of Kamareddine, Nederpelt, and Laan. We refereed this paper and found it useful for checking their examples to write our own independent (...)
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  41. Joseph S. Fulda (2006). Abstracts From Logical Form: An Experimental Study of the Nexus Between Language and Logic II. Journal of Pragmatics 38 (6):925-943.score: 24.0
    This experimental study provides further support for a theory of meaning first put forward by Bar-Hillel and Carnap in 1953 and foreshadowed by Asimov in 1951. The theory is the Popperian notion that the meaningfulness of a proposition is its a priori falsity. We tested this theory in the first part of this paper by translating to logical form a long, tightly written, published text and computed the meaningfulness of each proposition using the a priori falsity measure. We then selected (...)
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  42. Douglas S. Bridges (1978). A Note on Morse's Lambda‐Notation in Set Theory. Mathematical Logic Quarterly 24 (8):113-114.score: 24.0
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  43. S. Dennis, M. S. Humphreys & J. Wiles (1996). Mathematical Constraints on a Theory of Human Memory - Response. Behavioral and Brain Sciences 19 (3):559-560.score: 24.0
    Colonius suggests that, in using standard set theory as the language in which to express our computational-level theory of human memory, we would need to violate the axiom of foundation in order to express meaningful memory bindings in which a context is identical to an item in the list. We circumvent Colonius's objection by allowing that a list item may serve as a label for a context without being identical to that context. This debate serves to highlight the value of (...)
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  44. Wilfried Buchholz (1991). Notation Systems for Infinitary Derivations. Archive for Mathematical Logic 30 (5-6):277-296.score: 24.0
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  45. Gerhard Jäger (1984). Ρ-Inaccessible Ordinals, Collapsing Functions and a Recursive Notation System. Archive for Mathematical Logic 24 (1):49-62.score: 24.0
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  46. Noriya Kadota (1993). On Wainer's Notation for a Minimal Subrecursive Inaccessible Ordinal. Mathematical Logic Quarterly 39 (1):217-227.score: 24.0
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  47. Harold N. Lee (1931). The Meaning of the Notation of Mathematics and Logic. The Monist 41 (4):594-617.score: 24.0
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  48. Tom McCallion (2002). The Basic Price Spread Ratio. Journal of Macrodynamic Analysis 2.score: 24.0
    This essay endeavours to follow my reading of the argument in Bernard Lonergan’s quite brief discussion of the above topic, to be found in Macroeconomic Dynamics: An Essay in Circulation Analysis, Collected Works of Bernard Lonergan 15 (Toronto: Toronto University Press, 1999), as §28 (pages 156-162). Apart from minor changes in notation, etc., and some greater detail in the use of mathematical arguments, there is little that is novel in what is offered. It merely reflects what I found (...)
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  49. Zdzisław Pawlar (1963). Organization of Addressless Computers Working in Parenthesis Notation. Mathematical Logic Quarterly 9 (16‐17):243-249.score: 24.0
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