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Arnold W. Miller [26]Arnold V. Miller [5]Arnold Miller [4]Arnold I. Miller [3]
  1.  18
    Infinite Combinatorics and Definability.Arnold W. Miller - 1989 - Annals of Pure and Applied Logic 41 (2):179-203.
  2.  31
    Sacks Forcing, Laver Forcing, and Martin's Axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
    In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.
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  3. A Minimal Degree Which Collapses Ω1.Tim Carlson, Kenneth Kunen & Arnold W. Miller - 1984 - Journal of Symbolic Logic 49 (1):298-300.
    We consider a well-known partial order of Prikry for producing a collapsing function of minimal degree. Assuming MA + ≠ CH, every new real constructs the collapsing map.
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  4.  12
    Selective Covering Properties of Product Spaces.Arnold W. Miller, Boaz Tsaban & Lyubomyr Zdomskyy - 2014 - Annals of Pure and Applied Logic 165 (5):1034-1057.
    We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals.Our methods include the projection method introduced by the authors in an earlier work, as well as several new methods. Some special consequences of our main results are : Every product of a concentrated space with a Hurewicz S1S1 space satisfies S1S1. On the other hand, assuming the Continuum Hypothesis, (...)
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  5.  26
    Michael Canjar. Countable Ultraproducts Without CH. Annals of Pure and Applied Logic, Vol. 37 , Pp. 1–79. - R. Michael Canjar. Small Filter Forcing. The Journal of Symbolic Logic, Vol. 51 , Pp. 526–546. [REVIEW]Arnold W. Miller - 1991 - Journal of Symbolic Logic 56 (1):343-344.
  6. Mapping a Set of Reals Onto the Reals.Arnold W. Miller - 1983 - Journal of Symbolic Logic 48 (3):575-584.
    In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω 1.
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  7.  20
    Saharon Shelah, Can You Take Solovay's Inaccessible Away?Israel Journal of Mathematics, Vol. 48 , Pp. 1–47. - Jean Raisonnier, A Mathematical Proof of S. Shelah's Theorem on the Measure Problem and Related Results, Israel Journal of Mathematics, Vol. 48 , Pp. 48–56. [REVIEW]Arnold W. Miller - 1989 - Journal of Symbolic Logic 54 (2):633-635.
  8. Hegel's Philosophy of Nature Being Part Two of the Encyclopaedia of the Philosophical Sciences.Georg Wilhelm Friedrich Hegel, Karl Ludwig Michelet & Arnold V. Miller (eds.) - 1970 - Clarendon Press.
  9.  22
    Descriptive Set Theory Over Hyperfinite Sets.H. Jerome Keisler, Kenneth Kunen, Arnold Miller & Steven Leth - 1989 - Journal of Symbolic Logic 54 (4):1167-1180.
    The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.
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  10.  62
    Set Theoretic Properties of Loeb Measure.Arnold W. Miller - 1990 - Journal of Symbolic Logic 55 (3):1022-1036.
    In this paper we ask the question: to what extent do basic set theoretic properties of Loeb measure depend on the nonstandard universe and on properties of the model of set theory in which it lies? We show that, assuming Martin's axiom and κ-saturation, the smallest cover by Loeb measure zero sets must have cardinality less than κ. In contrast to this we show that the additivity of Loeb measure cannot be greater than ω 1 . Define $\operatorname{cof}(H)$ as the (...)
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  11.  10
    On the Borel Classification of the Isomorphism Class of a Countable Model.Arnold W. Miller - 1983 - Notre Dame Journal of Formal Logic 24 (1):22-34.
  12.  14
    The Baire Category Theorem and Cardinals of Countable Cofinality.Arnold W. Miller - 1982 - Journal of Symbolic Logic 47 (2):275-288.
    Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, other (...)
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  13.  45
    On Translating Hegel.Arnold V. Miller - 1983 - The Owl of Minerva 14 (3):6-7.
    Anyone who aims to translate Hegel into readable English should bear in mind what he said in an early essay, viz. that before the living spirit which dwells in a philosophy can reveal itself it must be brought to birth by a kindred spirit. His approach to Hegel will therefore be sympathetic and in order to grasp the full import of what he is saying will try to think along with him, will try to become, as G.R.G. Mure said, an (...)
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  14.  16
    On Relatively Analytic and Borel Subsets.Arnold W. Miller - 2005 - Journal of Symbolic Logic 70 (1):346 - 352.
    Define z to be the smallest cardinality of a function f: X → Y with X. Y ⊆ 2ω such that there is no Borel function g ⊇ f. In this paper we prove that it is relatively consistent with ZFC to have b < z where b is, as usual, smallest cardinality of an unbounded family in ωω. This answers a question raised by Zapletal. We also show that it is relatively consistent with ZFC that there exists X ⊆ (...)
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  15.  5
    The Number of Translates of a Closed Nowhere Dense Set Required to Cover a Polish Group.Arnold W. Miller & Juris Steprāns - 2006 - Annals of Pure and Applied Logic 140 (1):52-59.
    For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach (...)
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  16.  24
    Laver Richard. On the Consistency of Borel's Conjecture. Acta Mathematica, Vol. 137 No. 3–4 , Pp. 151–169.Baumgartner James E. And Laver Richard. Iterated Perfect-Set Forcing. Annals of Mathematical Logic, Vol. 17 , Pp. 271–288. [REVIEW]Arnold W. Miller - 1983 - Journal of Symbolic Logic 48 (3):882-883.
  17.  13
    Projective Subsets of Separable Metric Spaces.Arnold W. Miller - 1990 - Annals of Pure and Applied Logic 50 (1):53-69.
    In this paper we will consider two possible definitions of projective subsets of a separable metric space X. A set A subset of or equal to X is Σ11 iff there exists a complete separable metric space Y and Borel set B subset of or equal to X × Y such that A = {x ε X : there existsy ε Y ε B}. Except for the fact that X may not be completely metrizable, this is the classical definition of (...)
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  18.  24
    A Dedekind Finite Borel Set.Arnold W. Miller - 2011 - Archive for Mathematical Logic 50 (1-2):1-17.
    In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if ${B\subseteq 2^\omega}$ is a G δσ -set then either B is countable or B contains a perfect subset. Second, we prove that if 2 ω is the countable union of countable sets, then there exists an F σδ set ${C\subseteq 2^\omega}$ such that C is uncountable but contains no perfect subset. Finally, (...)
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  19.  23
    The Γ-Borel Conjecture.Arnold W. Miller - 2004 - Archive for Mathematical Logic 44 (4):425-434.
    .In this paper we prove that it is consistent that every γ-set is countable while not every strong measure zero set is countable. We also show that it is consistent that every strong γ-set is countable while not every γ-set is countable. On the other hand we show that every strong measure zero set is countable iff every set with the Rothberger property is countable.
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  20.  34
    Universal Sets for Pointsets Properly on the N Th Level of the Projective Hierarchy.Greg Hjorth, Leigh Humphries & Arnold W. Miller - 2013 - Journal of Symbolic Logic 78 (1):237-244.
    The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.
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  21.  34
    Absolute Knowing and the Destiny of the Individual.Arnold V. Miller - 1983 - The Owl of Minerva 15 (1):45-50.
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  22.  9
    Evolution and Ecology: The Pace of Life by K. D. Bennett.Arnold I. Miller - 1998 - Complexity 4 (1):48-49.
  23.  10
    Review: Saharon Shelah, Can You Take Solovay's Inaccessible Away?; Jean Raisonnier, A Mathematical Proof of S. Shelah's Theorem on the Measure Problem and Related Results. [REVIEW]Arnold W. Miller - 1989 - Journal of Symbolic Logic 54 (2):633-635.
  24.  7
    Morley Michael. The Number of Countable Models.Arnold W. Miller - 1984 - Journal of Symbolic Logic 49 (1):314-315.
  25.  8
    The Major Transitions in Evolution.Arnold I. Miller - 1997 - Complexity 2 (5):40-41.
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  26.  7
    A Minimal Degree Which Collapses $Omega_1$.Tim Carlson, Kenneth Kunen & Arnold W. Miller - 1984 - Journal of Symbolic Logic 49 (1):298-300.
    We consider a well-known partial order of Prikry for producing a collapsing function of minimal degree. Assuming $MA + \neq CH$, every new real constructs the collapsing map.
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  27.  10
    Orthogonal Families of Real Sequences.Arnold W. Miller & Juris Steprans - 1998 - Journal of Symbolic Logic 63 (1):29-49.
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  28.  5
    Review: Michael Canjar, Countable Ultraproducts Without CH; R. Michael Canjar, Small Filter Forcing. [REVIEW]Arnold W. Miller - 1991 - Journal of Symbolic Logic 56 (1):343-344.
  29.  4
    Long Borel Hierarchies.Arnold W. Miller - 2008 - Mathematical Logic Quarterly 54 (3):307-322.
    We show that there is a model of ZF in which the Borel hierarchy on the reals has length ω2. This implies that ω1 has countable cofinality, so the axiom of choice fails very badly in our model. A similar argument produces models of ZF in which the Borel hierarchy has exactly λ + 1 levels for any given limit ordinal λ less than ω2. We also show that assuming a large cardinal hypothesis there are models of ZF in which (...)
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  30.  4
    Review: Michael Morley, The Number of Countable Models. [REVIEW]Arnold W. Miller - 1984 - Journal of Symbolic Logic 49 (1):314-315.
  31.  3
    Hegel's Philosophy of Nature.Arnold V. Miller & J. N. Findlay (eds.) - 1970 - Oxford University Press.
    This is a much-needed reissue of the standard English translation of Hegel's Philosophy of Nature, originally published in 1970. The Philosophy of Nature is the second part of Hegel's Encyclopaedia of the Philosophical Sciences, all of which is now available in English from OUP. Hegel's aim in this work is to interpret the varied phenomena of Nature from the standpoint of a dialectical logic. Those who still think of Hegel as a merely a priori philosopher will here find abundant evidence (...)
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  32. Philosophy of Mind. Being Part Three of the Encyclopaedia of the Philosophical Sciences, 1830, Translated by William Wallace, Together with the Zusätze in Boumann's Text, 1845, Translated by A.V. Miller. With a Foreword by J.N. Findlay. --. [REVIEW]Georg Wilhelm Friedrich Hegel, William Wallace & Arnold V. Miller - 1971 - Clarendon Press.
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  33. Book and Software Reviews-Evolution and Ecology: The Pace of Life.Arnold I. Miller - 1998 - Complexity 4 (1):48.