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James E. Baumgartner [50]James Baumgartner [3]
  1.  6
    Set Theory. An Introduction to Independence Proofs.James E. Baumgartner & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (2):462.
  2.  13
    Iterated Perfect-Set Forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
  3.  15
    Remarks on Superatomic Boolean Algebras.James E. Baumgartner & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (2):109-129.
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  4.  3
    A New Class of Order Types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
  5.  12
    Almost-Disjoint Sets the Dense Set Problem and the Partition Calculus.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (4):401-439.
  6.  21
    Adjoining Dominating Functions.James E. Baumgartner & Peter Dordal - 1985 - Journal of Symbolic Logic 50 (1):94-101.
    If dominating functions in ω ω are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every well-ordered unbounded family of increasing functions is a scale, and the splitting number s (and hence the distributivity number h) remains at ω 1.
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  7.  3
    On the Size of Closed Unbounded Sets.James E. Baumgartner - 1991 - Annals of Pure and Applied Logic 54 (3):195-227.
    We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ = κ+n for n ε ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3 < ωω13 and every closed unbounded subsetof [ω3]<ω2 has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under a large (...)
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  8.  22
    On Splitting Stationary Subsets of Large Cardinals.James E. Baumgartner, Alan D. Taylor & Stanley Wagon - 1977 - Journal of Symbolic Logic 42 (2):203-214.
    Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ + -saturated, i.e., are there κ + stationary subsets of κ with pairwise intersections nonstationary? Our first observation is: Theorem. NS is κ + -saturated iff for every normal ideal J on κ there is a stationary set $A \subseteq \kappa$ such that $J = NS \mid A = \{X \subseteq (...)
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  9.  33
    Ultrafilters on Ω.James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):624-639.
    We study the I-ultrafilters on ω, where I is a collection of subsets of a set X, usually R or ω 1 . The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.
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  10.  11
    Ultrafilters on $Omega$.James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):624-639.
    We study the $I$-ultrafilters on $\omega$, where $I$ is a collection of subsets of a set $X$, usually $\mathbb{R}$ or $\omega_1$. The $I$-ultrafilters usually contain the $P$-points, often as a small proper subset. We study relations between $I$-ultrafilters for various $I$, and closure of $I$-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether $I$-ultrafilters always exist.
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  11.  27
    E. M. Kleinberg The Independence of Ramsey's Theorem. The Journal of Symbolic Logic, Vol. 34 , Pp. 205–206.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):462.
  12.  19
    Independence and Consistency Proofs in Quadratic Form Theory.James E. Baumgartner & Otmar Spinas - 1991 - Journal of Symbolic Logic 56 (4):1195-1211.
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  13.  16
    Chains and Antichains in P(Ω).James E. Baumgartner - 1980 - Journal of Symbolic Logic 45 (1):85-92.
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  14.  18
    Solomon Feferman. Some Applications of the Notions of Forcing and Generic Sets . The Theory of Models, Proceedings of the 1963 International Symposium at Berkeley, Edited by J. W. Addison, Leon Henkin, and Alfred Tarski, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam1965, Pp. 89–95. - Solomon Feferman. Some Applications of the Notions of Forcing and Generic Sets. Fundamenta Mathematicae, Vol. 56 No. 3 , Pp. 325–345. [REVIEW]James E. Baumgartner - 1972 - Journal of Symbolic Logic 37 (3):612-613.
  15.  18
    E. M. Kleinberg. Strong Partition Properties for Infinite Cardinals. The Journal of Symbolic Logic, Vol. 35 , Pp. 410–428.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):463.
  16.  17
    Thomas Jech and Karel Prikry. On Ideals of Sets and the Power Set Operation. Bulletin of the American Mathematical Society, Vol. 82 , Pp. 593–595. - F. Galvin, T. Jech, and M. Magidor. An Ideal Game. The Journal of Symbolic Logic, Vol. 43 , Pp. 284–292. - T. Jech, M. Magidor, W. Mitchell, and K. Prikry. Precipitous Ideals. The Journal of Symbolic Logic, Vol. 45 , Pp. 1–8. - Yuzuru Kakuda. On a Condition for Cohen Extensions Which Preserve Precipitous Ideals. The Journal of Symbolic Logic, Vol. 46, Pp. 296–300. - Thomas Jech and Karel Prikry. Ideals Over Uncountable Sets: Application of Almost Disjoint Functions and Generic Ultrapowers. Memoirs of the American Mathematical Society, No. 214. American Mathematical Society, Providence 1979, Iii + 71 Pp. - Menachem Magidor. Precipitous Ideals and Sets. Israel Journal of Mathematics, Vol. 35 , Pp. 109–134. [REVIEW]James E. Baumgartner - 1985 - Journal of Symbolic Logic 50 (1):239-240.
  17.  5
    Generalized Erdoös Cardinals and O4.James E. Baumgartner & Fred Galvin - 1978 - Annals of Mathematical Logic 15 (3):289-313.
  18.  16
    Saharon Shelah and Lee Stanley. A Theorem and Some Consistency Results in Partition Calculus. Annals of Pure Applied Logic, Vol. 36 , Pp. 119–152. [REVIEW]James E. Baumgartner - 1990 - Journal of Symbolic Logic 55 (2):888-889.
  19.  15
    J. W. Addison and Yiannis N. Moschovakis. Some Consequences of the Axiom of Definable Determinateness. Proceedings of the National Academy of Sciences, Vol. 59 , Pp. 708–712. - Donald A. Martin. The Axiom of Determinateness and Reduction Principles in the Analytical Hierarchy. Bulletin of the American Mathematical Society, Vol. 74 , Pp. 687–689. [REVIEW]James E. Baumgartner - 1973 - Journal of Symbolic Logic 38 (2):334.
  20.  15
    E. M. Kleinberg and R. A. Shore. On Large Cardinals and Partition Relations. The Journal of Symbolic Logic, Vol. 36 , Pp. 305–308.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):463.
  21.  15
    Edwin W. Miller. On a Property of Families of Sets. English with Polish Summary. Sprawozdania Z Posiedzeń Towarzystwa Naukowego Warszawskiego , Class III, Vol. 30 , Pp. 31–38. - Ben Dushnik and Miller E. W.. Partially Ordered Sets. American Journal of Mathematics, Vol. 63 , Pp. 600–610. - P. Erdős. Some Set-Theoretical Properties of Graphs. Revista, Universidad Nacional de Tucumán, Serie A, Matemáticas y Física Teórica, Vol. 3 , Pp. 363–367. - G. Fodor. Proof of a Conjecture of P. Erdős. Acta Scientiarum Mathematicarum, Vol. 14 No. 4 , Pp. 219–227. - P. Erdős and Rado R.. A Partition Calculus in Set Theory. Bulletin of the American Mathematical Society, Vol. 62 , Pp. 427–489. - P. Erdős and Rado R.. Intersection Theorems for Systems of Sets. The Journal of the London Mathematical Society, Vol. 35 , Pp. 85–90. - A. Hajnal. Some Results and Problems on Set Theory. Acta Mathematica Academiae Scientiarum Hungaricae, Vol. 11 , Pp. 277–298. - P. Erdős and Hajnal A.. On a Property of Families. [REVIEW]James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):698-701.
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  22.  10
    Generic Graph Construction.James E. Baumgartner - 1984 - Journal of Symbolic Logic 49 (1):234-240.
    It is shown that if ZF is consistent, then so is ZFC + GCH + "There is a graph with cardinality ℵ 2 and chromatic number ℵ 2 such that every subgraph of cardinality ≤ ℵ 1 has chromatic number ≤ ℵ 0 ". This partially answers a question of Erdos and Hajnal.
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  23.  17
    The Hanf Number for Complete Lω1, Ω-Sentences (Without GCH).James E. Baumgartner - 1974 - Journal of Symbolic Logic 39 (3):575 - 578.
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  24.  9
    Kenneth Kunen. Elementary Embeddings and Infinitary Combinatorics. The Journal of Symbolic Logic, Vol. 36, No. 3 , Pp. 407–413.James E. Baumgartner - 1974 - Journal of Symbolic Logic 39 (2):331.
  25.  12
    A Diamond Example of an Ordinal Graph with No Infinite Paths.James E. Baumgartner & Jean A. Larson - 1990 - Annals of Pure and Applied Logic 47 (1):1-10.
  26.  34
    Canonical Partition Relations.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (4):541-554.
    Several canonical partition theorems are obtained, including a simultaneous generalization of Neumer's lemma and the Erdos-Rado theorem. The canonical partition relation for infinite cardinals is completely determined, answering a question of Erdos and Rado. Counterexamples are given showing that in several ways these results cannot be improved.
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  27.  24
    In Memoriam: Paul Erdős 1913–1996.James E. Baumgartner - 1997 - Bulletin of Symbolic Logic 3 (1):70-72.
  28.  18
    Polarized Partition Relations.James E. Baumgartner & Andras Hajnal - 2001 - Journal of Symbolic Logic 66 (2):811-821.
    It is shown that for any cardinal $\kappa, \dbinom{(2^{ , and if κ is weakly compact $\dbinom{\kappa^+}{\kappa} \rightarrow \dbinom{\kappa}{\kappa}_{.
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  29.  26
    The Future of Modern Set Theory.James E. Baumgartner - 1994 - Annals of the Japan Association for Philosophy of Science 8 (4):187-190.
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  30.  18
    Maximal Subgroups of Infinite Symmetric Groups.James E. Baumgartner, Saharon Shelah & Simon Thomas - 1992 - Notre Dame Journal of Formal Logic 34 (1):1-11.
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  31.  17
    Mycielski Jan and Steinhaus H.. A Mathematical Axiom Contradicting the Axiom of Choice. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 10 , Pp. 1–3.Mycielski Jan. On the Axiom of Determinateness. Fundamenta Mathematicae, Vol. 53 , Pp. 205–224.Mycielski Jan and Świerczkowski S.. On the Lebesgue Measurability and the Axiom of Determinateness. Fundamenta Mathematicae, Vol. 54 , Pp. 67–71.Mycielski Jan. On the Axiom of Determinateness . Fundamenta Mathematicae, Vol. 59 , Pp. 203–212. [REVIEW]James E. Baumgartner - 1971 - Journal of Symbolic Logic 36 (1):164-166.
  32.  10
    [Omnibus Review].James E. Baumgartner - 1985 - Journal of Symbolic Logic 50 (1):239-240.
    Reviewed Works:Edwin W. Miller, On a Property of Families of Sets.Ben Dushnik, E. W. Miller, Partially Ordered Sets.P. Erdos, Some Set-theoretical Properties of Graphs.G. Fodor, Proof of a Conjecture of P. Erdos.P. Erdos, R. Rado, A Partition Calculus in Set Theory.P. Erdos, R. Rado, Intersection Theorems for Systems of Sets.A. Hajnal, Some Results and Problems on Set Theory.P. Erdos, A. Hajnal, On a Property of Families of Sets.A. Hajnal, Proof of a Conjecture of S. Ruziewicz.P. Erdos, A. Hajnal, R. Rado, (...)
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  33.  8
    Infinite Subscripts From Infinite Exponents.James E. Baumgartner & James M. Henle - 1984 - Journal of Symbolic Logic 49 (2):558-562.
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  34. Polarized Partition Relations and Almost-Disjoint Functions.James E. Baumgartner - 1989 - In Jens Erik Fenstad, Ivan Timofeevich Frolov & Risto Hilpinen (eds.), Logic, Methodology, and Philosophy of Science Viii: Proceedings of the Eighth International Congress of Logic, Methodology, and Philosophy of Science, Moscow, 1987. Sole Distributors for the U.S.A. And Canada, Elsevier Science.
  35.  14
    Review: E. M. Kleinberg, R. A. Shore, On Large Cardinals and Partition Relations. [REVIEW]James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):463-463.
  36.  8
    Kunen Kenneth. Set Theory. An Introduction to Independence Proofs. Studies in Logic and the Foundations of Mathematics, Vol. 102. North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1980, Xvi + 313 Pp. [REVIEW]James E. Baumgartner - 1986 - Journal of Symbolic Logic 51 (2):462-464.
  37.  8
    Ideals on Uncountable Cardinals.James E. Baumgartner, Alan Taylor, Stanley Wagon, Angus Macintyre, Leszek Pacholski & Jeff Paris - 2001 - Bulletin of Symbolic Logic 7 (1):79-79.
  38.  8
    Review: Saharon Shelah, Lee Stanley, A Theorem and Some Consistency Results in Partition Calculus. [REVIEW]James E. Baumgartner - 1990 - Journal of Symbolic Logic 55 (2):888-889.
  39.  6
    Review: J. W. Addison, Yiannis N. Moschovakis, Some Consequences of the Axiom of Definable Determinateness; Donald A. Martin, The Axiom of Determinateness and Reduction Principles in the Analytical Hierarchy. [REVIEW]James E. Baumgartner - 1973 - Journal of Symbolic Logic 38 (2):334-334.
  40. REVIEWS-Two Papers.James Baumgartner & Stevo Todorcevic - 2000 - Bulletin of Symbolic Logic 6 (4):497-497.
  41.  5
    Chains and Antichains in $Mathscr{P}(Omega)$.James E. Baumgartner - 1980 - Journal of Symbolic Logic 45 (1):85-92.
  42.  6
    Review: J. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory; Dana Scott, Foreword. [REVIEW]James E. Baumgartner - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
  43.  3
    Bell J. L.. Boolean-Valued Models and Independence Proofs in Set Theory. Second Edition of XLVI 165. Oxford Logic Guides, No. 12. Clarendon Press, Oxford University Press, Oxford and New York 1985, Xx + 165 Pp.Scott Dana. Foreword. A Revised Reprint of XLVI 165. Therein, Pp. Vii–Xiii. [REVIEW]James E. Baumgartner - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
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  44.  4
    Review: Solomon Feferman, J. W. Addison, Leon Henkin, Alfred Tarski, Some Applications of the Notions of Forcing and Generic Sets (Summary); Solomon Feferman, Some Applications of the Notions of Forcing and Generic Sets. [REVIEW]James E. Baumgartner - 1972 - Journal of Symbolic Logic 37 (3):612-613.
  45.  1
    Review: E. M. Kleinberg, Strong Partition Properties for Infinite Cardinals. [REVIEW]James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (3):463-463.
  46.  1
    The Hanf Number for Complete $L{Omega1, Omega}$-Sentences (Without GCH).James E. Baumgartner - 1974 - Journal of Symbolic Logic 39 (3):575-578.
  47.  1
    Review: Kenneth Kunen, Elementary Embeddings and Infinitary Combinatorics. [REVIEW]James E. Baumgartner - 1974 - Journal of Symbolic Logic 39 (2):331-331.