31 found
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  1.  6
    Set Theory. An Introduction to Independence Proofs.James E. Baumgartner & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (2):462.
  2.  1
    [Omnibus Review].Kenneth Kunen - 1969 - Journal of Symbolic Logic 34 (3):515-516.
  3.  40
    Elementary Embeddings and Infinitary Combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.
    One of the standard ways of postulating large cardinal axioms is to consider elementary embeddings,j, from the universe,V, into some transitive submodel,M. See Reinhardt–Solovay [7] for more details. Ifjis not the identity, andκis the first ordinal moved byj, thenκis a measurable cardinal. Conversely, Scott [8] showed that wheneverκis measurable, there is suchjandM. If we had assumed, in addition, that, thenκwould be theκth measurable cardinal; in general, the wider we assumeMto be, the largerκmust be.
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  4.  11
    Frege Structures and the Notions of Proposition, Truth and Set.Peter Aczel, Jon Barwise, H. Jerome Keisler & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (1):244-246.
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  5.  22
    Saturated Ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
  6. 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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  7. On Descendingly Incomplete Ultrafilters.Kenneth Kunen & Karel Prikry - 1971 - Journal of Symbolic Logic 36 (4):650-652.
  8.  9
    Hanf Numbers for Fragments of L ∞Ω.Jon Barwise & Kenneth Kunen - 1984 - Journal of Symbolic Logic 49 (1):315-315.
  9. The Real Line in Elementary Submodels of Set Theory.Kenneth Kunen & Franklin D. Tall - 2000 - Journal of Symbolic Logic 65 (2):683-691.
    Keywords: Elementary Submodel; Real Line; Order-Isomorphic.
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  10. Implicit Definability and Infinitary Languages.Kenneth Kunen - 1968 - Journal of Symbolic Logic 33 (3):446-451.
  11.  19
    Cohen Paul J.. Set Theory and the Continuum Hypothesis. W. A. Benjamin, Inc., New York and Amsterdam 1966, Vi + 154 Pp. [REVIEW]Kenneth Kunen - 1970 - Journal of Symbolic Logic 35 (4):591-592.
  12.  18
    Herbert B. Enderton. Elements of Set Theory. Academic Press, New York, San Francisco, and London, 1977, Xiv + 279 Pp. [REVIEW]Kenneth Kunen - 1981 - Journal of Symbolic Logic 46 (1):164-165.
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  13.  16
    J. R. Shoenfield. Measurable Cardinals. Logic Colloquium '69, Proceedings of the Summer School and Colloquium in Mathematical Logic, Manchester, August 1969, Edited by R. O. Gandy and C. E. M. Yates, Studies in Logic and the Foundations of Mathematics, Vol. 61, North-Holland Publishing Company, Amsterdam and London1971, Pp. 19–49. [REVIEW]Kenneth Kunen - 1975 - Journal of Symbolic Logic 40 (1):93-94.
  14.  50
    The Kleene Symposium and the Summer Meeting of the Association for Symbolic Logic, Madison 1978.John Addison, Jon Barwise, H. Jerome Keisler, Kenneth Kunen & Yiannis N. Moschovakis - 1979 - Journal of Symbolic Logic 44 (3):469-480.
  15.  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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  16.  16
    XVI. A Model for the Negation of the Axiom of Choice.Kenneth Kunen - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 489--494.
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  17.  11
    P. Vopěnka. The Limits of Sheaves and Applications on Constructions of Models. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 13 , Pp. 189–192. - P. Vopěnka. On ∇-Model of Set Theory. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 13 , Pp. 267–272. - P. Vopěnka. Properties of ∇-Model. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 13 , Pp. 441–444. - P. Vopěnka and P. Hájek. Permutation Submodels of the Model ∇. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 13 , Pp. 611–614. - P. Hájek and P. Vopěnka. Some Permutation Submodels of the Model ∇. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 14 , Pp. 1–7. - P. Vopěnka. ∇-Models in Which the Generalized Conti. [REVIEW]Kenneth Kunen - 1969 - Journal of Symbolic Logic 34 (3):515-516.
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  18.  32
    On a Combinatorial Property of Menas Related to the Partition Property for Measures on Supercompact Cardinals.Kenneth Kunen & Donald H. Pelletier - 1983 - Journal of Symbolic Logic 48 (2):475-481.
    T. K. Menas [4, pp. 225-234] introduced a combinatorial property χ (μ) of a measure μ on a supercompact cardinal κ and proved that measures with this property also have the partition property. We prove here that Menas' property is not equivalent to the partition property. We also show that if α is the least cardinal greater than κ such that P κ α bears a measure without the partition property, then α is inaccessible and Π 2 1 -indescribable.
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  19.  28
    Where Ma First Fails.Kenneth Kunen - 1988 - Journal of Symbolic Logic 53 (2):429-433.
    If θ is any singular cardinal of cofinality ω 1 , we produce a forcing extension in which MA holds below θ but fails at θ. The failure is due to a partial order which splits a gap of size θ in P(ω).
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  20.  31
    Annual Meeting of the Association for Symbolic Logic: Saint Louis, 1977.Jon Barwise, Kenneth Kunen & Joseph Ullian - 1978 - Journal of Symbolic Logic 43 (2):365-372.
  21. The Kleene Symposium: Proceedings of the Symposium Held June 18-24, 1978 at Madison, Wisconsin, U.S.A.Stephen Cole Kleene, Jon Barwise, H. Jerome Keisler & Kenneth Kunen (eds.) - 1980 - Sole Distributors for the U.S.A. And Canada, Elsevier North-Holland.
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  22.  15
    Review: Herbert B. Enderton, Elements of Set Theory. [REVIEW]Kenneth Kunen - 1981 - Journal of Symbolic Logic 46 (1):164-165.
  23.  29
    Gregory Trees, the Continuum, and Martin's Axiom.Kenneth Kunen & Dilip Raghavan - 2009 - Journal of Symbolic Logic 74 (2):712-720.
    We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory trees.
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  24.  1
    Where MA First Fails.Kenneth Kunen - 1988 - Journal of Symbolic Logic 53 (2):429-433.
  25.  10
    Carnegie Mellon University, Pittsburgh, PA May 19–23, 2004.John Baldwin, Lev Beklemishev, Michael Hallett, Valentina Harizanov, Steve Jackson, Kenneth Kunen, Angus J. MacIntyre, Penelope Maddy, Joe Miller & Michael Rathjen - 2005 - Bulletin of Symbolic Logic 11 (1).
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  26.  9
    Review: Paul J. Cohen, Set Theory and the Continuum Hypothesis. [REVIEW]Kenneth Kunen - 1970 - Journal of Symbolic Logic 35 (4):591-592.
  27.  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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  28.  6
    Review: J. R. Shoenfield, Measurable Cardinals. [REVIEW]Kenneth Kunen - 1975 - Journal of Symbolic Logic 40 (1):93-94.
  29.  1
    Madison 1970 Meeting of the Association for Symbolic Logic.H. Jerome Keisler & Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (2):368-378.
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  30.  17
    Some Applications of Iterated Ultrapowers in Set Theory.Kenneth Kunen - 1970 - Annals of Pure and Applied Logic 1 (2):179.
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  31.  22
    Set Theory and the Continuum Hypothesis.Kenneth Kunen - 1966 - Journal of Symbolic Logic 35 (4):591-592.
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