Search results for 'M. Timur Friedman' (try it on Scholar)

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  1. H. Friedman (1995). Sheard, M., See Friedman, H. Annals of Pure and Applied Logic 71:307.score: 1460.0
     
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  2. Harvey Friedman, A Complete Theory of Everything: Satisfiability in the Universal Domain Harvey M. Friedman October 10, 1999 Friedman@Math.Ohio-State.Edu Www.Math.Ohio-State.Edu/~Friedman/. [REVIEW]score: 1260.0
    Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
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  3. Harvey Friedman, A Complete Theory of Everything: Satisfiability in the Universal Domain Harvey M. Friedman October 10, 1999 Friedman@Math.Ohio-State.Edu. [REVIEW]score: 1260.0
    Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
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  4. Edwina L. Rissland, David B. Skalak & M. Timur Friedman (1997). Evaluating a Legal Argument Program: The BankXX Experiments. [REVIEW] Artificial Intelligence and Law 5 (1-2):1-74.score: 870.0
    In this article we evaluate the BankXX program from several perspectives. BankXX is a case-based legal argument program that retrieves cases and other legal knowledge pertinent to a legal argument through a combination of heuristic search and knowledge-based indexing. The program is described in detail in a companion article in Artificial Intelligence and Law 4: 1--71, 1996. Three perspectives are used to evaluate BankXX:(1) classical information retrieval measures of precision and recall applied against a hand-coded baseline; (2) knowledge-representation and case-based (...)
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  5. Edwina L. Rissland, David B. Skalak & M. Timur Friedman (1996). BankXX: Supporting Legal Arguments Through Heuristic Retrieval. [REVIEW] Artificial Intelligence and Law 4 (1):1-71.score: 870.0
    The BankXX system models the process of perusing and gathering information for argument as a heuristic best-first search for relevant cases, theories, and other domain-specific information. As BankXX searches its heterogeneous and highly interconnected network of domain knowledge, information is incrementally analyzed and amalgamated into a dozen desirable ingredients for argument (called argument pieces), such as citations to cases, applications of legal theories, and references to prototypical factual scenarios. At the conclusion of the search, BankXX outputs the set of argument (...)
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  6. Harvey M. Friedman, Friedman@Math.Ohio-State.Edu.score: 540.0
    It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.
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  7. Harvey Friedman, 4:00 P.M., F Sep 20.score: 360.0
    There are many familiar theorems whose proofs use methods which are in some appropriate sense substantially more "abstract" than its statement. Some particularly well known examples come from the use of complex variables in number theory. Sometimes such abstraction can be removed - for example by the "elementary proof of the prime number theorem" - and sometimes no appropriate removal is known. The interest in removing abstraction typically varies, with no agreed upon criteria for appropriateness. E.g., the removal might sacrifice (...)
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  8. Hannah Friedman (2011). Mining (A.M.) Hirt Imperial Mines and Quarries in the Roman World. Organizational Aspects 27 BC – AD 235. Pp. Xiv + 551, Maps. Oxford: Oxford University Press, 2010. Cased £80. ISBN: 978-0-19-957287-8. [REVIEW] The Classical Review 61 (02):612-613.score: 360.0
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  9. Sy D. Friedman (1992). Martin Donald A.. The Largest Countable This, That, and the Other. Cabal Seminar 79–81, Proceedings, Caltech-UCLA Logic Seminar 1979–81, Edited by Kechris AS, Martin DA, and Moschovakis YN, Lecture Notes in Mathematics, Vol. 1019, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983, Pp. 97–106. Kechris Alexander S., Martin Donald A., and Solovay Robert M.. Introduction to Q-Theory. Cabal Seminar 79–81, Proceedings, Caltech-UCLA Logic Seminar 1979–81, Edited by Kechris AS, Martin DA, and .. [REVIEW] Journal of Symbolic Logic 57 (1):262-264.score: 360.0
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  10. Sy D. Friedman (1992). Review: Donald A. Martin, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, The Largest Countable This, That, and the Other; Alexander S. Kechris, Donald A. Martin, Robert M. Solovay, Introduction to $Q$-Theory; Steve Jackson, A. S. Kechris, D. A. Martin, J. R. Steel, AD and the Projective Ordinals. [REVIEW] Journal of Symbolic Logic 57 (1):262-264.score: 360.0
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  11. S. D. Friedman, W. G. Handley, S. S. Wainer, A. Joyal, I. Moerdijk, L. Newelski, F. van Engelen & J. van Oosten (1994). Downey, R., Gasarch, W. And Moses, M., The Structure. Annals of Pure and Applied Logic 70:287.score: 360.0
     
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  12. Harvey Friedman, Ramsey Theory and Enormous Lower Bounds.score: 300.0
    by Harvey M. Friedman Department of Mathematics Ohio State University friedman@math.ohio-state.edu www.math.ohio-state.edu/~friedman/ April 5, 1997..
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  13. Harvey M. Friedman, Foundations of Mathematics: Past, Present, and Future.score: 300.0
    It turns out, time and time again, in order to make serious progress in f.o.m., we need to take actual reasoning and actual development into account at precisely the proper level. If we take these into account too much, then we are faced with information that is just too difficult to create an exact science around - at least at a given state of development of f.o.m. And if we take these into account too little, our findings will not have (...)
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  14. Harvey M. Friedman, Concept Calculus: Much Better Than.score: 240.0
    This is the initial publication on Concept Calculus, which establishes mutual interpretability between formal systems based on informal commonsense concepts and formal systems for mathematics through abstract set theory. Here we work with axioms for "better than" and "much better than", and the Zermelo and Zermelo Frankel axioms for set theory.
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  15. Harvey M. Friedman, The Upper Shift Kernel Theorems.score: 240.0
    We now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.
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  16. Harvey M. Friedman, Remarks On GÖDel Phenomena and the Field of Reals.score: 240.0
    A lot of the well known impact of the Gödel phenomena is in the form of painful messages telling us that certain major mathematical programs cannot be completed as intended. This aspect of Gödel – the delivery of bad news –is not welcomed, and defensive measures are now in place.
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  17. Harvey M. Friedman, Sentential Reflection.score: 240.0
    We present two forms of “sentential reflection”, which are shown to be mutually interpretable with Z2 and ZFC, respectively.
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  18. Harvey M. Friedman, Strict Reverse Mathematics.score: 240.0
    An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...)
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  19. Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel (2000). Does Mathematics Need New Axioms? Bulletin of Symbolic Logic 6 (4):401-446.score: 240.0
    Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...)
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  20. Harvey M. Friedman, Kernel Structure Theory.score: 240.0
    We have been recently engaged in this search, and have announced a long series of successively simpler and more convincing examples. See [Fr09-10].
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  21. Harvey M. Friedman, Vigre Lectures.score: 240.0
    In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.
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  22. Harvey M. Friedman, Unprovable Theorems.score: 240.0
    I don’t remember if I got as high as 2-390, but I distinctly remember taking my first logic course - as a Freshman - with Hartley Rogers, in Fall 1964 - here in 2-190. Or was it in 2-290?
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  23. Harvey M. Friedman, From Russell's Paradox To.score: 240.0
    Russell’s way out of his paradox via the impredicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.
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  24. Harvey M. Friedman, What Are These Three Aspects?score: 240.0
    Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.
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  25. Harvey M. Friedman, Remarks On the Unknowable.score: 240.0
    The kind of unknowability I will discuss concerns the count of certain natural finite sets of objects. Even the situation with regard to our present strong formal systems is rather unclear. One can just profitably focus on that, putting aside issues of general unknowability.
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  26. Harvey M. Friedman, Similar Subclasses.score: 240.0
    Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.
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  27. Harvey M. Friedman, Philosophy 532 Philosophical Problems in Logic Lecture 1 9/25/02.score: 240.0
    This is widely accepted, inside and outside philosophy, but one can spend an entire career clarifying, justifying, and amplifying on this statement. Certainly a graduate student career.
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  28. Harvey M. Friedman, Concrete Mathematical Incompleteness.score: 240.0
    there are mathematical statements that cannot be proved or refuted using the usual axioms and rules of inference of mathematics.
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  29. Harvey M. Friedman, Decision Problems in Strings and Formal Methods.score: 240.0
    We focus on two formal methods contexts which generate investigations into decision problems for finite strings.
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  30. Harvey M. Friedman, Agenda.score: 240.0
    In the Foundational Life, philosophy is commonly used as a method for choosing and analyzing fundamental concepts, and mathematics is commonly used for rigorous development. The mathematics informs the philosophy and the philosophy informs the mathematics.
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  31. Harvey M. Friedman, Quadratic Axioms.score: 240.0
    We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.
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  32. Harvey M. Friedman, Boolean Relation Theory.score: 240.0
    BRT is always based on a choice of BRT setting. A BRT setting is a pair (V,K), where V is an interesting family of multivariate functions. K is an interesting family of sets. In this talk, we will only consider V,K, where V is an interesting family of multivariate functions from N into N. K is an interesting family of subsets of N.
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  33. Harvey M. Friedman, Issues in the Foundations of Mathematics.score: 240.0
    C. To what extent, and in what sense, is the natural hierarchy of logical strengths rep resented by familiar systems ranging from exponential function arithmetic to ZF + j:V Æ V robust?
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  34. Harvey M. Friedman, Philosophy 536 Philosophy of Mathematics Lecture 1 9/25/02.score: 240.0
    This distinction between logic and mathematics is subject to various criticisms and can be given various defenses. Nevertheless, the division seems natural enough and is commonly adopted in presentations of the standard foundations for mathematics.
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  35. Harvey M. Friedman, Equational Representations.score: 240.0
    We begin by presenting the language L(N,℘N,℘℘N). This is the standard language for presenting third order sentences, using its intended interpretation.
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  36. Harvey M. Friedman, Shocking(?) Unprovability.score: 240.0
    Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.
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  37. Harvey M. Friedman, Transfer Principles in Set Theory.score: 240.0
    1. Transfer principles from N to On. A. Mahlo cardinals. B. Weakly compact cardinals. C. Ineffable cardinals. D. Ramsey cardinals. E. Ineffably Ramsey cardinals. F. Subtle cardinals. G. From N to (...))
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  38. Harvey M. Friedman, Adjacent Ramsey Theory.score: 240.0
    Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.
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  39. Harvey M. Friedman, Decision Problems in Euclidean Geometry.score: 240.0
    We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hilbert's Tenth Problem. The limited number of facts used from recursion theory are isolated at the beginning.
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  40. Alan M. Leslie, Ori Friedman & Tim P. German (2004). Core Mechanisms in 'Theory of Mind'. Trends in Cognitive Sciences 8 (12):528-533.score: 240.0
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  41. Harvey M. Friedman, A Complete Theory of Everything: Satisfiability in the Universal Domain.score: 240.0
    Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
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  42. Harvey M. Friedman, Concrete Incompleteness From Efa Through Large Cardinals.score: 240.0
    Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.
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  43. Harvey M. Friedman, Decision Procedures for Verification.score: 240.0
    We focus on two formal methods contexts which generate investigations into decision problems for finite strings.
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  44. Harvey M. Friedman, P 1 INCOMPLETENESS: Finite Set Equations.score: 240.0
    We say that R is strictly dominating if and only if for all x,yŒ[1,n], if R(x,y) then max(x) 3k ¥ [1,n], there exists A Õ [1,n] such that R = A. Furthermore, A Õ [1,n] is unique.
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  45. Harvey M. Friedman, Strict Reverse Mathematics Draft.score: 240.0
    NOTE: This is an expanded version of my lecture at the special session on reverse mathematics, delivered at the Special Session on Reverse Mathematics held at the Atlanta AMS meeting, on January 6, 2005.
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  46. Harvey M. Friedman, Clay Millenium Problem: P = Np.score: 240.0
    The equation P = NP concerns algorithms for deciding membership in sets. The consensus is that P ≠ NP, although some prominent experts guess otherwise.
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  47. Harvey M. Friedman, Foundational Adventures for the Future.score: 240.0
    • Wright Brothers made a two mile flight • Wright Brothers made a 42 mile flight • Want to ship goods • Want to move lots of passengers • Want reliability and safety • Want low cost • ... Modern aviation • Each major advance spawns reasonable demands for more and more • Excruciating difficulties overcome • Armies of people over decades or more • Same story for any practically any epoch breaking advance in anything..
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  48. Harvey M. Friedman, Introduction.score: 240.0
    The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).
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  49. Harvey M. Friedman, Geometry Axioms.score: 240.0
    To prove this, we fix P(x) to be any polynomial of degree ≥ 1 with a positive and negative value. We define a critical interval to be any nonempty open interval on which P is strictly monotone and where P is not strictly monotone on any larger open interval. Here an open interval may not have endpoints in F, and may be infinite on the left or right or both sides. Obviously, the critical intervals are pairwise disjoint.
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  50. Harvey M. Friedman, P01 INCOMPLETENESS: Finite Set Equations.score: 240.0
    Let R Õ [1,n]3k ¥ [1,n]k. We define R = {y Œ [1,n]k:($xŒA3)(R(x,y))}. We say that R is strictly dominating if and only if for all x,yŒ[1,n]k, if R(x,y) then max(x) < max(y).
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