Results for 'Maximal set'

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  1.  10
    -Maximal Sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
    Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us (...)
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  2. R ‐Maximal Sets and Q1,N‐Reducibility.Roland Sh Omanadze & Irakli O. Chitaia - forthcoming - Mathematical Logic Quarterly.
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  3.  8
    Some Properties of R-Maximal Sets and Q 1,N -Reducibility.R. Sh Omanadze - 2015 - Archive for Mathematical Logic 54 (7-8):941-959.
    We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and (...)
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  4.  10
    Some Properties of Maximal Sets.Roland S. H. Omanadze & Irakli O. Chitaia - 2015 - Logic Journal of the IGPL 23 (4):628-639.
  5.  22
    Diagonals and D-Maximal Sets.Eberhard Herrmann & Martin Kummer - 1994 - Journal of Symbolic Logic 59 (1):60-72.
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  6.  10
    Diagonals and $Mathscr{D}$-Maximal Sets.Eberhard Herrmann & Martin Kummer - 1994 - Journal of Symbolic Logic 59 (1):60-72.
  7.  10
    ${\cal D}$-Maximal Sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
    Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us (...)
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  8.  10
    A Co-Analytic Maximal Set of Orthogonal Measures.Vera Fischer & Asger Törnquist - 2010 - Journal of Symbolic Logic 75 (4):1403-1414.
    We prove that if V = L then there is a $\Pi _{1}^{1}$ maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.
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  9.  13
    Gerald E. Sacks. A Maximal Set Which is Not Complete. Michigan Mathematical Journal, Vol. 11 , Pp. 193–205.K. Appel - 1968 - Journal of Symbolic Logic 32 (4):528.
  10.  48
    Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration Without Duplication.Richard M. Friedberg - 1958 - Journal of Symbolic Logic 23 (3):309-316.
  11.  24
    Cardinally Maximal Sets of Non-Equivalent Order Types.Charles Fefferman - 1967 - Mathematical Logic Quarterly 13 (13-14):205-212.
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  12. Some Theorems on R-Maximal Sets and Major Subsets of Recursively Enumerable Sets.Manuel Lerman - 1971 - Journal of Symbolic Logic 36 (2):193-215.
  13.  14
    A Theorem on Maximal Sets.Joseph S. Ullian - 1961 - Notre Dame Journal of Formal Logic 2 (4):222-223.
  14. On the Filter of Computably Enumerable Supersets of an R-Maximal Set.Steffen Lempp, André Nies & D. Reed Solomon - 2001 - Archive for Mathematical Logic 40 (6):415-423.
    We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).
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  15. Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
    In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification (...)
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  16.  10
    The Approachability Ideal Without a Maximal Set.John Krueger - 2019 - Annals of Pure and Applied Logic 170 (3):297-382.
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  17.  6
    Invariant Constructions of Simple and Maximal Sets.Frank P. Weber - 1995 - Mathematical Logic Quarterly 41 (2):143-160.
    The main results of the present paper are the following theorems: 1. There is no e ∈ ω such that for any A, B ⊆ ω, SA = Wmath image is simple in A, and if A′ [TRIPLE BOND]TB′, then SA =* SB. 2 There is an e ∈ ω such that for any A, B ⊆ ω, MA = We is incomplete maximal in A, and if A =* B, then MA [TRIPLE BOND]TMB.
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  18.  15
    Maximal Non-Trivial Sets of Instances of Your Least Favorite Logical Principle.Lucas Rosenblatt - 2020 - Journal of Philosophy 117 (1):30-54.
    The paper generalizes Van McGee's well-known result that there are many maximal consistent sets of instances of Tarski's schema to a number of non-classical theories of truth. It is shown that if a non-classical theory rejects some classically valid principle in order to avoid the truth-theoretic paradoxes, then there will be many maximal non-trivial sets of instances of that principle that the non-classical theorist could in principle endorse. On the basis of this it is argued that the idea (...)
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  19.  19
    1-Reducibility Inside an M-Degree with Maximal Set.E. Herrmann - 1992 - Journal of Symbolic Logic 57 (3):1046-1056.
    The structure of the l-degrees included in an m-degree with a maximal set together with the l-reducibility relation is characterized. For this a special sublattice of the lattice of recursively enumerable sets under the set-inclusion is used.
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  20.  47
    Σ2 Induction and Infinite Injury Priority Argument, Part I: Maximal Sets and the Jump Operator.C. T. Chong & Yue Yang - 1998 - Journal of Symbolic Logic 63 (3):797 - 814.
    Related Works: Part II: C. T. Chong, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part II: Tame $\Sigma_2$ Coding and the Jump Operator. Ann. Pure Appl. Logic, vol. 87, no. 2, 103--116. Mathematical Reviews : MR1490049 Part III: C. T. Chong, Lei Qian, Theodore A. Slaman, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part III: Prompt Sets, Minimal Paries and Shoenfield's Conjecture. Mathematical Reviews : MR1818378.
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  21.  18
    Soare Robert I.. Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets. Annals of Mathematics, Ser. 2 Vol. 100 , Pp. 80–120. - Lerman Manuel and Soare Robert I.. D-Simple Sets, Small Sets, and Degree Classes. Pacific Journal of Mathematics, Vol. 87 , Pp. 135–155. - Cholak Peter. Automorphisms of the Lattice of Recursively Enumerable Sets. Memoirs of the American Mathematical Society, No. 541. American Mathematical Society, Providence1995, Viii + 151 Pp. - Harrington Leo and Soare Robert I.. The Δ30-Automorphism Method and Noninvariant Classes of Degrees. Journal of the American Mathematical Society, Vol. 9 , Pp. 617–666. [REVIEW]Rod Downey - 1997 - Journal of Symbolic Logic 62 (3):1048-1055.
  22.  11
    Review: Gerald E. Sacks, A Maximal Set Which is Not Complete. [REVIEW]K. Appel - 1967 - Journal of Symbolic Logic 32 (4):528-528.
  23.  22
    Turing Degrees and Many-One Degrees of Maximal Sets.Manuel Lerman - 1970 - Journal of Symbolic Logic 35 (1):29-40.
  24. Maximal Consistent Sets of Instances of Tarski’s Schema.Vann McGee - 1992 - Journal of Philosophical Logic 21 (3):235 - 241.
  25.  6
    Ullian Joseph S.. A Theorem on Maximal Sets. Notre Dame Journal of Formal Logic, Vol. 2 Pp. 222–223.Steven Orey - 1962 - Journal of Symbolic Logic 27 (2):244-244.
  26.  9
    Review: Richard M. Friedberg, Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration Without Duplication. [REVIEW]Marian Boykan Pour-El - 1960 - Journal of Symbolic Logic 25 (2):165-166.
  27.  5
    Review: Joseph S. Ullian, A Theorem on Maximal Sets. [REVIEW]Steven Orey - 1962 - Journal of Symbolic Logic 27 (2):244-244.
  28. Maximally Consistent Sets of Instances of Naive Comprehension.Luca Incurvati & Julien Murzi - 2017 - Mind 126 (502).
    Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...)
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  29.  34
    Maximal God: A New Defence of Perfect Being Theism.Yujin Nagasawa - 2017 - Oxford University Press.
    Yujin Nagasawa presents a new, stronger version of perfect being theism, the conception of God as the greatest possible being. Nagasawa argues that God should be understood, not as omniscient, omnipotent, and omnibenevolent, but rather as a being that has the maximal consistent set of knowledge, power, and benevolence.
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  30.  95
    The Modal Logic of Set-Theoretic Potentialism and the Potentialist Maximality Principles.Joel David Hamkins & Øystein Linnebo - 2022 - Review of Symbolic Logic 15 (1):1-35.
    We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, (...)
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  31.  1
    Wellfoundedness proof with the maximal distinguished set.Toshiyasu Arai - forthcoming - Archive for Mathematical Logic:1-25.
    In Arai it is shown that an ordinal \\) is an upper bound for the proof-theoretic ordinal of a set theory \\). In this paper we show that a second order arithmetic \ proves the wellfoundedness up to \\) for each N. It is easy to interpret \ in \\).
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  32. Maximality Vs. Extendability: Reflections on Structuralism and Set Theory.Geoffrey Hellman - unknown
    In a recent paper, while discussing the role of the notion of analyticity in Carnap’s thought, Howard Stein wrote: “The primitive view–surely that of Kant–was that whatever is trivial is obvious. We know that this is wrong; and I would put it that the nature of mathematical knowledge appears more deeply mysterious today than it ever did in earlier centuries – that one of the advances we have made in philosophy has been to come to an understanding of just ∗I (...)
     
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  33.  16
    Maximal Compact Subgroups in the o-Minimal Setting.Annalisa Conversano - 2013 - Journal of Mathematical Logic 13 (1):1350004.
    A characterization of groups definable in o-minimal structures having maximal definable definably compact subgroups is given. This follows from a definable decomposition in analogy with Lie groups, where the role of maximal tori is played by maximal 0-subgroups. Along the way we give structural theorems for solvable groups, linear groups, and extensions of definably compact by torsion-free definable groups.
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  34.  10
    Set‐Aside Cells in Maximal Indirect Development: Evolutionary and Developmental Significance.Kevin J. Peterson, R. Andrew Cameron & Eric H. Davidson - 1997 - Bioessays 19 (7):623-631.
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  35.  11
    Maximizing Resources: Ensuring Standard of Care for a Transgender Child in a Rural Setting.Jacqueline J. Glover & Daniel H. Reirden - 2019 - American Journal of Bioethics 19 (7):66-67.
    Volume 19, Issue 7, July 2019, Page 66-67.
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  36.  7
    Rationality and Maximal Consistent Sets for a Fragment of ASPIC + Without Undercut.Jesse Heyninck & Christian Straßer - 2021 - Argument and Computation 12 (1):3-47.
    Structured argumentation formalisms, such as ASPIC +, offer a formal model of defeasible reasoning. Usually such formalisms are highly parametrized and modular in order to provide a unifying framework in which different forms of reasoning can be expressed. This generality comes at the price that, in their most general form, formalisms such as ASPIC + do not satisfy important rationality postulates, such as non-interference. Similarly, links to other forms of knowledge representation, such as reasoning with maximal consistent sets of (...)
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  37.  2
    Complexity of Rule Sets in Mining Incomplete Data Using Characteristic Sets and Generalized Maximal Consistent Blocks.Patrick G. Clark, Cheng Gao, Jerzy W. Grzymala-Busse, Teresa Mroczek & Rafal Niemiec - 2021 - Logic Journal of the IGPL 29 (2):124-137.
    In this paper, missing attribute values in incomplete data sets have three possible interpretations: lost values, attribute-concept values and ‘do not care’ conditions. For rule induction, we use characteristic sets and generalized maximal consistent blocks. Therefore, we apply six different approaches for data mining. As follows from our previous experiments, where we used an error rate evaluated by ten-fold cross validation as the main criterion of quality, no approach is universally the best. Thus, we decided to compare our six (...)
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  38.  6
    How General Practitioners Decide on Maxims of Action in Response to Demands From Conflicting Sets of Norms: A Grounded Theory Study.Linus Johnsson & Lena Nordgren - 2019 - BMC Medical Ethics 20 (1):33.
    The work of general practitioners is infused by norms from several movements, of which evidence based medicine, patient-centredness, and virtue ethics are some of the most influential. Their precepts are not clearly reconcilable, and structural factors may limit their application. In this paper, we develop a conceptual framework that explains how GPs respond, across different fields of interaction in their daily work, to the pressure exerted by divergent norms. Data was generated from unstructured interviews with and observations of sixteen Swedish (...)
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  39.  1
    Maximal N-Disjointed Sets and the Axiom of Choice.C. C. Chang - 1970 - Journal of Symbolic Logic 35 (3):473-473.
  40.  8
    Degrees of Recursively Enumerable Sets Which Have No Maximal Supersets.A. H. Lachlan - 1968 - Journal of Symbolic Logic 33 (3):431-443.
  41.  9
    Health Research Priority Setting: A Duty to Maximize Social Value?Douglas MacKay - 2018 - American Journal of Bioethics 18 (11):25-26.
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  42.  10
    Normativity in Perception.Maxime Doyon & Thiemo Breyer (eds.) - 2015 - Palgrave-Macmillan.
    Human activity is permeated by norms of all sorts: moral norms provide the 'code' for what we ought to do, norms of logic regulate how we ought to reason, scientific norms set the standards for what counts as knowledge, legal norms determine what is lawfully permitted and what isn't, aesthetic norms establish canons of beauty and shape artistic trends and practices, and socio-cultural norms provide criteria for what counts as tolerable, just, praiseworthy, or unacceptable in a community or milieu. Given (...)
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  43.  9
    A Proof of Hechler's Theorem on Embedding $\aleph_1$ -Directed Sets Cofinally Into $$.Maxim R. Burke - 1997 - Archive for Mathematical Logic 36 (6):399-403.
    . We give a proof of Hechler's theorem that any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\aleph_1$\end{document}-directed partial order can be embedded via a ccc forcing notion cofinally into \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\omega^\omega$\end{document} ordered by eventual dominance. The proof relies on the standard forcing relation rather than the variant introduced by Hechler.
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  44.  6
    The Hyperuniverse Project and Maximality.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.) - 2018 - Basel, Switzerland: Birkhäuser.
    This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John (...)
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  45.  40
    Powers of the Ideal of Lebesgue Measure Zero Sets.Maxim R. Burke - 1991 - Journal of Symbolic Logic 56 (1):103-107.
    We investigate the cofinality of the partial order N κ of functions from a regular cardinal κ into the ideal N of Lebesgue measure zero subsets of R. We show that when add(N) = κ and the covering lemma holds with respect to an inner model of GCH, then cf(N κ ) = max {cf(κ κ ), cf([ cf(N)] κ )}. We also give an example to show that the covering assumption cannot be removed.
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  46.  27
    C. C. Chang. Maximal N-Disjointed Sets and the Axiom of Choice. Fundamenta Mathematicae, Vol. 49 , Pp. 11–14.Azriel Lévy - 1970 - Journal of Symbolic Logic 35 (3):473.
  47.  12
    Optimizing the Initial Setting of Complex Adaptive Systems-Optimizing the Layout of Initial AFVs Stations for Maximizing the Diffusion of AFVs.Jiangjiang Zhao & Tieju Ma - 2016 - Complexity 21 (S1):275-290.
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  48.  6
    Α-Degrees of Maximal Α-R.E. Sets.Anne Leggett - 1978 - Journal of Symbolic Logic 43 (3):456-474.
  49. Tree Forcing and Definable Maximal Independent Sets in Hypergraphs.Jonathan Schilhan - forthcoming - Journal of Symbolic Logic:1-35.
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  50.  11
    Review: C. C. Chang, Maximal $N$-Disjointed Sets and the Axiom of Choice. [REVIEW]Azriel Levy - 1970 - Journal of Symbolic Logic 35 (3):473-473.
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