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  1. Borel Sets and Ramsey's Theorem.Fred Galvin & Karel Prikry - 1973 - Journal of Symbolic Logic 38 (2):193-198.
  2.  15
    On the Singular Cardinals Problem.Jack Silver, Fred Galvin, Keith J. Devlin & R. B. Jensen - 1981 - Journal of Symbolic Logic 46 (4):864-866.
  3.  6
    Generalized Erdoös Cardinals and O4.James E. Baumgartner & Fred Galvin - 1978 - Annals of Mathematical Logic 15 (3):289-313.
  4.  12
    Borel's Conjecture in Topological Groups.Fred Galvin & Marion Scheepers - 2013 - Journal of Symbolic Logic 78 (1):168-184.
    We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number $\kappa$, let ${\sf BC}_{\kappa}$ denote this generalization. Then ${\sf BC}_{\aleph_0}$ is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture, $\neg{\sf BC}_{\aleph_1}$ is equivalent to the existence of a Kurepa tree of height $\aleph_1$. Using the connection of ${\sf BC}_{\kappa}$ with a generalization of Kurepa's Hypothesis, we obtain the following consistency results: 1. If it is consistent that there is a 1-inaccessible cardinal then it is (...)
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  5.  6
    Baire Spaces and Infinite Games.Fred Galvin & Marion Scheepers - 2016 - Archive for Mathematical Logic 55 (1-2):85-104.
    It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.
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  6.  9
    Grätzer G.. On the Class of Subdirect Powers of a Finite Algebra. Acta Scientiarum Mathematicarum, Vol. 25 , Pp. 160–168. [REVIEW]Fred Galvin - 1972 - Journal of Symbolic Logic 37 (1):189-189.
  7.  2
    Éršov Ü. L.. Razréšimost′ eléméntarnoj téorii distributivnyh struktur s otnositél′nyml dopolnéniámi i téorii fil′trov . Algébra i logika, Séminar, vol. 3 no. 3 pp. 17–38. [REVIEW]Fred Galvin - 1969 - Journal of Symbolic Logic 34 (1):126-126.
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  8.  3
    Review: U. L. Ersov, Decidability of the Elementary Theory of Relatively Complemented Distributive Lattices and of the Theory of Filters. [REVIEW]Fred Galvin - 1969 - Journal of Symbolic Logic 34 (1):126-126.
  9.  9
    Strong Measure Zero and Infinite Games.Fred Galvin, Jan Mycielski & Robert M. Solovay - 2017 - Archive for Mathematical Logic 56 (7-8):725-732.
    We show that strong measure zero sets -totally bounded metric space) can be characterized by the nonexistence of a winning strategy in a certain infinite game. We use this characterization to give a proof of the well known fact, originally conjectured by K. Prikry, that every dense \ subset of the real line contains a translate of every strong measure zero set. We also derive a related result which answers a question of J. Fickett.
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