Arithmetic progressions of length three in subsets of a random set
Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)
Acta Arithmetica
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Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)
Acta Arithmetica
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Peter J. Grabner, Pierre Liardet (1999)
Acta Arithmetica
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Valentin Gutev, Haruto Ohta (2000)
Fundamenta Mathematicae
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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.
J. S. Hsia, M. I. Icaza (1999)
Acta Arithmetica
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Saharon Shelah, Oren Kolman (1996)
Fundamenta Mathematicae
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We assume a theory T in the logic is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.
Sy Friedman (1997)
Fundamenta Mathematicae
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We present a reformulation of the fine structure theory from Jensen [72] based on his Σ* theory for K and introduce the Fine Structure Principle, which captures its essential content. We use this theory to prove the Square and Fine Scale Principles, and to construct Morasses.