منابع مشابه
The Hereditarily Finite Sets
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...
متن کاملA remark on hereditarily nonparadoxical sets
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....
متن کاملOn hereditarily small sets in ZF
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...
متن کاملHereditarily Finite Sets in Constructive Type Theory
We axiomatize hereditarily finite sets in constructive type theory and show that all models of the axiomatization are isomorphic. The axiomatization takes the empty set and adjunction as primitives and comes with a strong induction principle. Based on the axiomatization, we construct the set operations of ZF and develop the basic theory of finite ordinals and cardinality. We construct a model o...
متن کاملFuzzy universal algebras on $L$-sets
This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1975
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700031487