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  1. 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}_{.
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  2. 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.
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  3. James E. Baumgartner (1997). In Memoriam: Paul Erdös, 1913-1996. Bulletin of Symbolic Logic 3 (1):70-72.
  4. 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.
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  5. 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.
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  6. James E. Baumgartner (1994). The Future of Modern Set Theory. Annals of the Japan Association for Philosophy of Science 8 (4):187-190.
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  7. James E. Baumgartner, Saharon Shelah & Simon Thomas (1992). Maximal Subgroups of Infinite Symmetric Groups. Notre Dame Journal of Formal Logic 34 (1):1-11.
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  8. 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 (...)
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  9. James E. Baumgartner & Otmar Spinas (1991). Independence and Consistency Proofs in Quadratic Form Theory. Journal of Symbolic Logic 56 (4):1195-1211.
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  10. 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.
  11. 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.
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  12. 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.
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  13. 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.
  14. James E. Baumgartner & Saharon Shelah (1987). Remarks on Superatomic Boolean Algebras. Annals of Pure and Applied Logic 33 (2):109-129.
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  15. 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.
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  16. James E. Baumgartner (1986). Review: Kenneth Kunen, Set Theory. An Introduction to Independence Proofs. [REVIEW] Journal of Symbolic Logic 51 (2):462-464.
  17. 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, (...)
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  18. 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.
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  19. 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.
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  20. James E. Baumgartner & James M. Henle (1984). Infinite Subscripts From Infinite Exponents. Journal of Symbolic Logic 49 (2):558-562.
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  21. James E. Baumgartner (1980). Chains and Antichains in P(Ω). Journal of Symbolic Logic 45 (1):85-92.
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  22. James E. Baumgartner (1980). Chains and Antichains in $Mathscr{P}(Omega)$. Journal of Symbolic Logic 45 (1):85-92.
  23. James E. Baumgartner & Richard Laver (1979). Iterated Perfect-Set Forcing. Annals of Mathematical Logic 17 (3):271-288.
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  24. James E. Baumgartner & Fred Galvin (1978). Generalized Erdoös Cardinals and O4. Annals of Mathematical Logic 15 (3):289-313.
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  25. 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 (...)
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  26. James E. Baumgartner (1976). A New Class of Order Types. Annals of Mathematical Logic 9 (3):187-222.
    No categories
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  27. James E. Baumgartner (1976). Almost-Disjoint Sets the Dense Set Problem and the Partition Calculus. Annals of Mathematical Logic 9 (4):401-439.
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  28. 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.
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  29. James E. Baumgartner (1975). Review: E. M. Kleinberg, Strong Partition Properties for Infinite Cardinals. [REVIEW] Journal of Symbolic Logic 40 (3):463-463.
  30. 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.
  31. James E. Baumgartner (1975). Review: E. M. Kleinberg, The Independence of Ramsey's Theorem. [REVIEW] Journal of Symbolic Logic 40 (3):462-462.
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  32. James E. Baumgartner (1974). Review: Kenneth Kunen, Elementary Embeddings and Infinitary Combinatorics. [REVIEW] Journal of Symbolic Logic 39 (2):331-331.
  33. James E. Baumgartner (1974). The Hanf Number for Complete Lω1, Ω-Sentences (Without GCH). Journal of Symbolic Logic 39 (3):575 - 578.
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  34. James E. Baumgartner (1974). The Hanf Number for Complete $L{Omega1, Omega}$-Sentences (Without GCH). Journal of Symbolic Logic 39 (3):575-578.
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  35. 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.
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  36. 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.
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