Results for 'analytic combinatorics'

988 found
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  1.  27
    Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results.Andreas Weiermann - 2005 - Annals of Pure and Applied Logic 136 (1):189-218.
    This paper is intended to give for a general mathematical audience a survey of intriguing connections between analytic combinatorics and logic. We define the ordinals below ε0 in non-logical terms and we survey a selection of recent results about the analytic combinatorics of these ordinals. Using a versatile and flexible compression technique we give applications to phase transitions for independence results, Hilbert’s basis theorem, local number theory, Ramsey theory, Hydra games, and Goodstein sequences. We discuss briefly (...)
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  2.  9
    Fuzzy logics – quantitatively.Marek Zaionc & Zofia Kostrzycka - 2023 - Journal of Applied Non-Classical Logics 34 (1):97-132.
    ABSTRACT The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n (...)
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  3.  21
    Fuzzy logics – quantitatively.Zofia Kostrzycka & Marek Zaionc - 2023 - Journal of Applied Non-Classical Logics 34 (1):97-132.
    The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n to (...)
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  4.  13
    Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory.Peter M. Schuster, Monika Seisenberger & Andreas Weiermann (eds.) - 2020 - Cham, Switzerland: Springer Verlag.
    This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and (...)
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  5.  4
    Current periodical articles.All Acceptable Generalizations are Analytic - 1977 - American Philosophical Quarterly 14 (3).
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  6. Las causas en aristoteles Y santo Tomas.Posterior Analytícs - 1983 - Sapientia 147:9.
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  7.  10
    2. Boolean algebras of the form P (co)/I and their automorphisms ([6, 5.Analytic Ideals - 1996 - Bulletin of Symbolic Logic 2 (3).
  8.  5
    Index locorum.Posterior Analytics - 2010 - In Richard Bett (ed.), The Cambridge Companion to Ancient Scepticism. New York: Cambridge University Press. pp. 370.
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  9. on Concept Formation.I. Aristotle & Posterior Analytics - 2010 - In David Charles (ed.), Definition in Greek philosophy. New York: Oxford University Press. pp. 424.
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  10. 2. Boolean algebras of the form P ()/I and their automorphisms ([6, 5, 19, 20]). 3. The equivalence relation associated with I: XEI Y iff X△ Y∈ I ([4, 14, 15, 9]). In Section 4, we will have an opportunity to state some consequences of our. [REVIEW]Analytic Ideals - 1996 - Bulletin of Symbolic Logic 2 (3).
  11. GT Csanady Department of Mechanical Engineering, University of Waterloo.Simple Analytical Models Of Wind-Driven - 1968 - In Peter Koestenbaum (ed.), Proceedings. [San Jose? Calif.,: [San Jose? Calif.. pp. 371.
     
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  12.  25
    Phase transitions for Gödel incompleteness.Andreas Weiermann - 2009 - Annals of Pure and Applied Logic 157 (2-3):281-296.
    Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano Arithmetic, Bull. of (...)
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  13.  21
    Tautologies over implication with negative literals.Hervé Fournier, Danièle Gardy, Antoine Genitrini & Marek Zaionc - 2010 - Mathematical Logic Quarterly 56 (4):388-396.
    We consider logical expressions built on the single binary connector of implication and a finite number of literals . We prove that asymptotically, when the number of variables becomes large, all tautologies have the following simple structure: either a premise equal to the goal, or two premises which are opposite literals.
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  14.  10
    Exact unprovability results for compound well-quasi-ordered combinatorial classes.Andrey Bovykin - 2009 - Annals of Pure and Applied Logic 157 (2-3):77-84.
    In this paper we prove general exact unprovability results that show how a threshold between provability and unprovability of a finite well-quasi-orderedness assertion of a combinatorial class is transformed by the sequence-construction, multiset-construction, cycle-construction and labeled-tree-construction. Provability proofs use the asymptotic pigeonhole principle, unprovability proofs use Weiermann-style compression techniques and results from analytic combinatorics.
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  15.  49
    Computer experiments in harmonic analysis.Michael Barany - unknown
    It is conventionally understood that computers play a rather limited role in theoretical mathematics. While computation is indispensable in applied mathematics and the theory of computing and algorithms is rich and thriving, one does not, even today, expect to find computers in theoretical mathematics settings beyond the theory of computing. Where computers are used, by those studying combinatorics , algebra, number theory, or dynamical systems, the computer most often assumes the role of an automated and speedy theoretician, performing manipulations (...)
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  16. Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets.Catalin Barboianu - 2006 - Craiova, Romania: Infarom.
    Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...)
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  17.  23
    Experimental mathematics.V. I. Arnolʹd - 2015 - Providence. Rhode Island: American Mathematical Society. Edited by D. B. Fuks & Mark E. Saul.
    One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...)
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  18.  5
    Recent advances in drug design methods: Where will they lead?Philip M. Dean - 1994 - Bioessays 16 (9):683-687.
    Drug design methods have made significant new advances over the last ten years, mainly in the areas of molecular modelling. In more recent times important developments in theory have led to a different type of modelling becoming possible, the so‐called de novo or automated design algorithms. In this new method the programs perform much of the chemist's thinking, in finding appropriately sized chemical groups to fit into a target site. However this is a combinatoric problem which has no general analytical (...)
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  19. The Combinatorics of Stoic Conjunction.Susanne Bobzien - 2011 - Oxford Studies in Ancient Philosophy 40:157-188.
    ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...)
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  20.  10
    Chance Combinatorics: The Theory that History Forgot.John D. Norton - 2023 - Perspectives on Science 31 (6):771-810.
    Seventeenth-century “chance combinatorics” was a self-contained theory. It had an objective notion of chance derived from physical devices with chance properties, such as casts of dice, combinatorics to count chances and, to interpret their significance, a rule for converting these counts into fair wagers. It lacked a notion of chance as a measure of belief, a precise way to connect chance counts with frequencies and a way to compare chances across different games. These omissions were not needed for (...)
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  21.  33
    Combinatorics for Small Ideals on Pkλ.Yoshihiro Abe - 1997 - Mathematical Logic Quarterly 43 (4):541-549.
    We study the distributivity of the bounded ideal on Pkλ and answer negatively to a question of Johnson in [13]. The size of non-normal ideals with the partition property is also studied.
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  22.  17
    Combinatorics and Graph Theory.John Harris, Jeffry L. Hirst & Michael Mossinghoff - 2008 - Springer.
    This book covers a wide variety of topics in combinatorics and graph theory.
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  23.  12
    Infinite combinatorics plain and simple.Dániel T. Soukup & Lajos Soukup - 2018 - Journal of Symbolic Logic 83 (3):1247-1281.
    We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our (...)
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  24.  11
    Borel combinatorics fail in HYP.Henry Towsner, Rose Weisshaar & Linda Westrick - 2022 - Journal of Mathematical Logic 23 (2).
    We characterize the completely determined Borel subsets of HYP as exactly the [Formula: see text] subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, (...)
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  25.  21
    The combinatorics of splittability.Boaz Tsaban - 2004 - Annals of Pure and Applied Logic 129 (1-3):107-130.
    Marion Scheepers, in his studies of the combinatorics of open covers, introduced the property asserting that a cover of type can be split into two covers of type . In the first part of this paper we give an almost complete classification of all properties of this form where and are significant families of covers which appear in the literature , using combinatorial characterizations of these properties in terms related to ultrafilters on . In the second part of the (...)
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  26.  19
    Combinatorics of first order structures and propositional proof systems.Jan Krajíček - 2004 - Archive for Mathematical Logic 43 (4):427-441.
    We define the notion of a combinatorics of a first order structure, and a relation of covering between first order structures and propositional proof systems. Namely, a first order structure M combinatorially satisfies an L-sentence Φ iff Φ holds in all L-structures definable in M. The combinatorics Comb(M) of M is the set of all sentences combinatorially satisfied in M. Structure M covers a propositional proof system P iff M combinatorially satisfies all Φ for which the associated sequence (...)
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  27.  41
    Some combinatorics of imperfect information.Peter Cameron & Wilfrid Hodges - 2001 - Journal of Symbolic Logic 66 (2):673-684.
  28.  35
    Infinite combinatorics and definability.Arnold W. Miller - 1989 - Annals of Pure and Applied Logic 41 (2):179-203.
  29.  24
    Combinatorics and probability: Six- to ten-year-olds reliably predict whether a relation will occur.Michel Gonzalez & Vittorio Girotto - 2011 - Cognition 120 (3):372-379.
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  30. Combinatorics as scientific method in the work of Ramon Llull and Gottfried Wilhelm Leibniz.Diane Doucet-Rosenstein - 2018 - In Armador Vega & Peter Weibel (eds.), Dia-logos: Ramon Llull's method of thought and artistic practice. Minneapolis, MN: University Of Minnesota Press.
     
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  31.  14
    Combinatoric strategies for genome mapping.Glen A. Evans - 1991 - Bioessays 13 (1):39-44.
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  32.  55
    Nonstandard combinatorics.Joram Hirshfeld - 1988 - Studia Logica 47 (3):221 - 232.
    Ramsey type theorems are theorems of the form: if certain sets are partitioned at least one of the parts has some particular property. In its finite form, Ramsey's theory will ask how big the partitioned set should be to assure this fact. Proofs of such theorems usually require a process of multiple choice, so that this apparently pure combinatoric field is rich in proofs that use ideal guides in making the choices. Typically they may be ultrafilters or points in the (...)
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  33.  16
    Combinatorics with definable sets: Euler characteristics and Grothendieck rings.Jan Krají Cek & Thomas Scanlon - 2000 - Bulletin of Symbolic Logic 6 (3):311-330.
    We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of (...)
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  34.  80
    Combinatorics with definable sets: Euler characteristics and grothendieck rings.Jan Krajíček & Thomas Scanlon - 2000 - Bulletin of Symbolic Logic 6 (3):311-330.
    We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of (...)
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  35. Some Combinatorics of Imperfect Information.Peter Cameron & Wilfrid Hodges - 2001 - Journal of Symbolic Logic 66 (2):673-684.
     
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  36.  18
    Infinitary combinatorics.E. M. Kleinberg - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 361--418.
  37.  52
    Combinatorics for the dominating and unsplitting numbers.Jason Aubrey - 2004 - Journal of Symbolic Logic 69 (2):482-498.
    In this paper we introduce a new property of families of functions on the Baire space, called pseudo-dominating, and apply the properties of these families to the study of cardinal characteristics of the continuum. We show that the minimum cardinality of a pseudo-dominating family is min{.
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  38.  22
    Combinatorics to Philosophy. The Legacy of G. C. Rota.E. Damiani, O. D'Antona, F. Palombi & V. Marra (eds.) - 2009 - Springer.
    Mathematical Essays in Honor of Gian-Carlo Rota, Boston, Basel, Berlin, ... Crapo, H. (1993), On the Anick-Rota Representation of the Bracket Ring of the ...
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  39.  30
    The combinatorics of combinatorial coding by a real.Saharon Shelah & Lee J. Stanley - 1995 - Journal of Symbolic Logic 60 (1):36-57.
    We lay the combinatorial foundations for [5] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.
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  40.  74
    Infinitary combinatorics and modal logic.Andreas Blass - 1990 - Journal of Symbolic Logic 55 (2):761-778.
    We show that the modal propositional logic G, originally introduced to describe the modality "it is provable that", is also sound for various interpretations using filters on ordinal numbers, for example the end-segment filters, the club filters, or the ineffable filters. We also prove that G is complete for the interpretation using end-segment filters. In the case of club filters, we show that G is complete if Jensen's principle □ κ holds for all $\kappa ; on the other hand, it (...)
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  41. Combinatorics on ideals and forcing with trees.Marcia J. Groszek - 1987 - Journal of Symbolic Logic 52 (3):582-593.
    Classes of forcings which add a real by forcing with branching conditions are examined, and conditions are found which guarantee that the generic real is of minimal degree over the ground model. An application is made to almost-disjoint coding via a real of minimal degree.
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  42.  15
    Cue Combinatorics in Memory Retrieval for Anaphora.Dan Parker - 2019 - Cognitive Science 43 (3):e12715.
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  43.  11
    The combinatorics of object recognition in cluttered environments using constrained search.W. Eric L. Grimson - 1990 - Artificial Intelligence 44 (1-2):121-165.
  44. Separating syntax and combinatorics in categorial grammar.Reinhard Muskens - 2007 - Research on Language and Computation 5 (3):267-285.
    The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data (...)
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  45.  22
    Combinatorics at ℵ ω.Dima Sinapova & Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (4):996-1007.
    We construct a model in which the singular cardinal hypothesis fails at ℵωℵω. We use characterizations of genericity to show the existence of a projection between different Prikry type forcings.
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  46.  12
    The Combinatorics of Tastes and Humours in Classical Indian Medicine and Mathematics.Dominik Wujastyk - 2000 - Journal of Indian Philosophy 28 (5/6):479-495.
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  47.  37
    Pκλ combinatorics II: The RK ordering beneath a supercompact measure.William S. Zwicker - 1986 - Journal of Symbolic Logic 51 (3):604 - 616.
    We characterize some large cardinal properties, such as μ-measurability and P 2 (κ)-measurability, in terms of ultrafilters, and then explore the Rudin-Keisler (RK) relations between these ultrafilters and supercompact measures on P κ (2 κ ). This leads to the characterization of 2 κ -supercompactness in terms of a measure on measure sequences, and also to the study of a certain natural subset, Full κ , of P κ (2 κ ), whose elements code measures on cardinals less than κ. (...)
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  48.  17
    Measurable combinatorics and orbit equivalence relations.Tomasz Cieśla - 2020 - Bulletin of Symbolic Logic 26 (3-4):300-301.
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  49.  25
    Combinatorics on large cardinals.E. Montenegro - 1992 - Journal of Symbolic Logic 57 (2):617-643.
  50.  9
    Definable combinatorics with dense linear orders.Himanshu Shukla, Arihant Jain & Amit Kuber - 2020 - Archive for Mathematical Logic 59 (5-6):679-701.
    We compute the model-theoretic Grothendieck ring, \\), of a dense linear order with or without end points, \\), as a structure of the signature \, and show that it is a quotient of the polynomial ring over \ generated by \\) by an ideal that encodes multiplicative relations of pairs of generators. This ring can be embedded in the polynomial ring over \ generated by \. As a corollary we obtain that a DLO satisfies the pigeon hole principle for definable (...)
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