48 found
Order:
  1.  17
    James E. Baumgartner (1994). The Future of Modern Set Theory. Annals of the Japan Association for Philosophy of Science 8 (4):187-190.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  2.  3
    James E. Baumgartner & Richard Laver (1979). Iterated Perfect-Set Forcing. Annals of Mathematical Logic 17 (3):271-288.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   15 citations  
  3. James E. Baumgartner (1976). A New Class of Order Types. Annals of Mathematical Logic 9 (3):187-222.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   18 citations  
  4.  4
    James E. Baumgartner & Saharon Shelah (1987). Remarks on Superatomic Boolean Algebras. Annals of Pure and Applied Logic 33 (2):109-129.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   10 citations  
  5. James E. Baumgartner (1991). On the Size of Closed Unbounded Sets. 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   11 citations  
  6.  3
    James E. Baumgartner (1976). Almost-Disjoint Sets the Dense Set Problem and the Partition Calculus. Annals of Mathematical Logic 9 (4):401-439.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   12 citations  
  7.  6
    James E. Baumgartner & Peter Dordal (1985). Adjoining Dominating Functions. 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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   8 citations  
  8.  10
    James E. Baumgartner (1995). Ultrafilters on Ω. 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.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  9.  12
    James E. Baumgartner (1974). The Hanf Number for Complete Lω1, Ω-Sentences (Without GCH). Journal of Symbolic Logic 39 (3):575 - 578.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  10.  9
    James E. Baumgartner, Alan D. Taylor & Stanley Wagon (1977). On Splitting Stationary Subsets of Large Cardinals. 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  11.  1
    James E. Baumgartner & Fred Galvin (1978). Generalized Erdoös Cardinals and O4. Annals of Mathematical Logic 15 (3):289-313.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  12.  6
    James E. Baumgartner (1980). Chains and Antichains in P(Ω). Journal of Symbolic Logic 45 (1):85-92.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  13.  8
    James E. Baumgartner & Otmar Spinas (1991). Independence and Consistency Proofs in Quadratic Form Theory. Journal of Symbolic Logic 56 (4):1195-1211.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  14.  5
    James E. Baumgartner (1984). Generic Graph Construction. 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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  15.  9
    James E. Baumgartner (1997). In Memoriam: Paul Erdös, 1913-1996. Bulletin of Symbolic Logic 3 (1):70-72.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  16.  4
    James E. Baumgartner & James M. Henle (1984). Infinite Subscripts From Infinite Exponents. Journal of Symbolic Logic 49 (2):558-562.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  17.  2
    James E. Baumgartner (1995). Ultrafilters on $Omega$. 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.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  18.  1
    James E. Baumgartner & Jean A. Larson (1990). A Diamond Example of an Ordinal Graph with No Infinite Paths. Annals of Pure and Applied Logic 47 (1):1-10.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  19.  10
    James E. Baumgartner & Andras Hajnal (2001). Polarized Partition Relations. 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}_{.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  20.  1
    James E. Baumgartner (1980). Chains and Antichains in $Mathscr{P}(Omega)$. Journal of Symbolic Logic 45 (1):85-92.
  21.  2
    James E. Baumgartner (1986). Review: Kenneth Kunen, Set Theory. An Introduction to Independence Proofs. [REVIEW] Journal of Symbolic Logic 51 (2):462-464.
  22.  2
    James E. Baumgartner (1972). 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] Journal of Symbolic Logic 37 (3):612-613.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  23.  7
    James E. Baumgartner (1975). Canonical Partition Relations. 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.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  24.  3
    James E. Baumgartner, Saharon Shelah & Simon Thomas (1992). Maximal Subgroups of Infinite Symmetric Groups. Notre Dame Journal of Formal Logic 34 (1):1-11.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  25.  1
    James E. Baumgartner (1975). Review: E. M. Kleinberg, The Independence of Ramsey's Theorem. [REVIEW] Journal of Symbolic Logic 40 (3):462-462.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  26.  1
    James E. Baumgartner (1975). Review: E. M. Kleinberg, R. A. Shore, On Large Cardinals and Partition Relations. [REVIEW] Journal of Symbolic Logic 40 (3):463-463.
  27.  1
    James E. Baumgartner (1986). Review: J. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory; Dana Scott, Foreword. [REVIEW] Journal of Symbolic Logic 51 (4):1076-1077.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  28.  1
    James E. Baumgartner (1985). [Omnibus Review]. 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, (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  29.  1
    James E. Baumgartner (1974). Review: Kenneth Kunen, Elementary Embeddings and Infinitary Combinatorics. [REVIEW] Journal of Symbolic Logic 39 (2):331-331.
  30. James E. Baumgartner (1973). Addison J. W. And Moschovakis Yiannis N.. Some Consequences of the Axiom of Definable Determinateness. Proceedings of the National Academy of Sciences, Vol. 59 , Pp. 708–712.Martin Donald A.. The Axiom of Determinateness and Reduction Principles in the Analytical Hierarchy. Bulletin of the American Mathematical Society, Vol. 74 , Pp. 687–689. [REVIEW] Journal of Symbolic Logic 38 (2):334.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  31. James E. Baumgartner (1986). 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] Journal of Symbolic Logic 51 (4):1076-1077.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  32. James E. Baumgartner (1972). Feferman Solomon. Some Applications of the Notions of Forcing and Generic Sets . The Theory of Models, Proceedings of the 1963 International Symposium at Berkeley, Edited by Addison J. W., Henkin Leon, and Tarski Alfred, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam 1965, Pp. 89–95.Feferman Solomon. Some Applications of the Notions of Forcing and Generic Sets. Fundamenta Mathematicae, Vol. 56 No. 3 , Pp. 325–345. [REVIEW] Journal of Symbolic Logic 37 (3):612-613.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  33. James E. Baumgartner, Alan Taylor, Stanley Wagon, Angus Macintyre, Leszek Pacholski & Jeff Paris (2001). Ideals on Uncountable Cardinals. Bulletin of Symbolic Logic 7 (1):79-79.
    Direct download  
     
    Export citation  
     
    My bibliography  
  34. James E. Baumgartner (1985). Jech Thomas and Prikry Karel. On Ideals of Sets and the Power Set Operation. Bulletin of the American Mathematical Society, Vol. 82 , Pp. 593–595.Galvin F., Jech T., and Magidor M.. An Ideal Game. [REVIEW] Journal of Symbolic Logic 50 (1):239-240.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  35. James E. Baumgartner (1975). Kleinberg E. M.. Strong Partition Properties for Infinite Cardinals. Journal of Symbolic Logic 40 (3):463.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  36. James E. Baumgartner (1975). Kleinberg E. M. The Independence of Ramsey's Theorem. Journal of Symbolic Logic 40 (3):462.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  37. James E. Baumgartner (1975). Kleinberg E. M. And Shore R. A.. On Large Cardinals and Partition Relations. Journal of Symbolic Logic 40 (3):463.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  38. James E. Baumgartner (1974). Kunen Kenneth. Elementary Embeddings and Infinitary Combinatorics. Journal of Symbolic Logic 39 (2):331.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  39. James E. Baumgartner (1986). 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] Journal of Symbolic Logic 51 (2):462-464.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  40. James E. Baumgartner (1995). Miller Edwin W.. On a Property of Families of Sets. English with Polish Summary. Sprawozdania Z Posiedzeń Towarzystwa Naukowego Warszawskiego , Class III, Vol. 30 , Pp. 31–38.Dushnik Ben and E. W. Miller. Partially Ordered Sets. American Journal of Mathematics, Vol. 63 , Pp. 600–610.Erdős P.. Some Set-Theoretical Properties of Graphs. Revista, Universidad Nacional de Tucumán, Serie A, Matemáticas y Física Teórica, Vol. 3 , Pp. 363–367.Fodor G.. Proof of a Conjecture of P. Erdős. Acta Scientiarum Mathematicarum, Vol. 14 No. 4 , Pp. 219–227.Erdős P. And R. Rado. A Partition Calculus in Set Theory. Bulletin of the American Mathematical Society, Vol. 62 , Pp. 427–489.Erdős P. And R. Rado. Intersection Theorems for Systems of Sets. The Journal of the London Mathematical Society, Vol. 35 , Pp. 85–90.Hajnal A.. Some Results and Problems on Set Theory. Acta Mathematica Academiae Scientiarum Hungaricae, Vol. 11 , Pp. 277–298.Erdős P. And A. Hajnal. On a Property of Families of Sets. Acta Mathem. [REVIEW] Journal of Symbolic Logic 60 (2):698-701.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  41. James E. Baumgartner (1971). 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] Journal of Symbolic Logic 36 (1):164-166.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  42. James E. Baumgartner (1989). Polarized Partition Relations and Almost-Disjoint Functions. 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
    Direct download  
     
    Export citation  
     
    My bibliography  
  43. James E. Baumgartner (1975). Review: E. M. Kleinberg, Strong Partition Properties for Infinite Cardinals. [REVIEW] Journal of Symbolic Logic 40 (3):463-463.
  44. James E. Baumgartner (1973). 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] Journal of Symbolic Logic 38 (2):334-334.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  45. James E. Baumgartner (1990). Review: Saharon Shelah, Lee Stanley, A Theorem and Some Consistency Results in Partition Calculus. [REVIEW] Journal of Symbolic Logic 55 (2):888-889.
  46. James E. Baumgartner (1990). Shelah Saharon and Stanley Lee. A Theorem and Some Consistency Results in Partition Calculus. Annals of Pure Applied Logic, Vol. 36 (1987), Pp. 119–152. [REVIEW] Journal of Symbolic Logic 55 (2):888-889.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  47. James E. Baumgartner & Kenneth Kunen (1986). Set Theory. An Introduction to Independence Proofs. Journal of Symbolic Logic 51 (2):462.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  48. James E. Baumgartner (1974). The Hanf Number for Complete $L{Omega1, Omega}$-Sentences (Without GCH). Journal of Symbolic Logic 39 (3):575-578.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography