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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his.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.
G. Hjorth (2000)
Fundamenta Mathematicae
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Non-abelian Polish groups arising as countable products of countable groups can be tame in arbitrarily complicated ways. This contrasts with some results of Solecki who revealed a very different picture in the abelian case.
N. Brunner, Paul Howard, Jean Rubin (1997)
Fundamenta Mathematicae
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Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.
Kurt Girstmair (1999)
Acta Arithmetica
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Zoran Spasojević (1995)
Fundamenta Mathematicae
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I prove that the statement that “every linear order of size can be embedded in ” is consistent with MA + ¬ wKH.