منابع مشابه
Elementary submodels in infinite combinatorics
We show that usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary submodels. We also present a new proof of Nash-Williams’s theorem on cycle-decomposition of graphs, and finally we obtain some new decomposition the...
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We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than 20 .
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Elementary submodels of some initial segment of the set-theoretic universe are useful in order to prove certain theorems in general topology as well as in algebra. As an illustration we give proofs of two theorems due to Arkhangel’skii concerning cardinal invariants of compact spaces.
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Given a space 〈X,J 〉 in an elementary submodel M of H(θ), define XM to be X ∩ M with the topology generated by {U ∩ M : U ∈ J ∩ M}. It is established, using anti-large-cardinals assumptions, that if XM is compact and its regular open algebra is isomorphic to that of a continuous image of some power of the two-point discrete space, then X = XM . Assuming CH+SCH (the Singular Cardinals Hypothesis...
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It is a truism that all of mathematics can be expressed in the language of set theory, i.e. the predicate calculus (including equality) with the single two-place relation ∈. As with any other countable language, the language of set theory is subject to the Löwenheim-Skolem Theorem, which asserts that if we have some axioms – e.g. the usual axioms of set theory (ZFC) – formulated in this languag...
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ژورنال
عنوان ژورنال: Open Mathematics
سال: 2014
ISSN: 2391-5455
DOI: 10.2478/s11533-013-0400-z