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The gap‐two cardinal problem for uncountable languages
Author(s) -
Villegas Silva Luis Miguel
Publication year - 2018
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201400079
Subject(s) - uncountable set , mathematics , predicate (mathematical logic) , unary operation , regular cardinal , axiom , discrete mathematics , axiom of choice , combinatorics , computer science , countable set , set theory , set (abstract data type) , programming language , geometry
In this paper we prove some cases of the gap‐2 cardinal transfer theorem for uncountable languages assuming the axiom of constructibility. Consider uncountable cardinals κ , λ , with λ regular, a first order language L with at least one unary predicate symbol U , with | L | < min { κ , λ } . Given an L ‐structure A = ⟨ A , U A , … ⟩ , where| A | = κ + +and| U A | = κ , we find an L ‐structure B = ⟨ B , U B , … ⟩ such that B ≡ A ,| B | = λ + +and| U B | = λ .