Hereditarily Lindelöf products and Luzin sets
نویسندگان
چکیده
منابع مشابه
More on rc-Lindelöf sets and almost rc-Lindelöf sets
A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...
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We will kill the old Luzin and Sierpinski sets in order to build a model where U (M) = U (N) = ℵ 1 and there are neither Luzin nor Sierpinski sets. Thus we answer a question of J. Steprans, communicated by S. Todorcevic on route from Evans to MSRI.
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The theory of hereditarily finite sets is formalised, following the development of Świerczkowski [2]. An HF set is a finite collection of other HF sets; they enjoy an induction principle and satisfy all the axioms of ZF set theory apart from the axiom of infinity, which is negated. All constructions that are possible in ZF set theory (Cartesian products, disjoint sums, natural numbers, function...
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Call a set A ⊆ R paradoxical if there are disjoint A0, A1 ⊆ A such that both A0 and A1 are equidecomposable with A via countabbly many translations. X ⊆ R is hereditarily nonparadoxical if no uncountable subset of X is paradoxical. Penconek raised the question if every hereditarily nonparadoxical set X ⊆ R is the union of countably many sets, each omitting nontrivial solutions of x − y = z − t....
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We show in ZF (the usual set theory without Choice) that for any set X, the collection of sets Y such that each element of the transitive closure of {Y } is strictly smaller in size than X (the collection of sets hereditarily smaller than X) is a set. This result has been shown by Jech in the case X = ω1 (where the collection under consideration is the set of hereditarily countable sets). In [2...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1994
ISSN: 0166-8641
DOI: 10.1016/0166-8641(94)90113-9