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Two Models that show the Interpolation Theorem Fails in all L 1 ( Q α ) and L 1, 1 ( Q α , α = 0, 1, 2,…
Author(s) -
Talebi Norollah
Publication year - 1992
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/24.4.305
Subject(s) - mathematics , interpolation (computer graphics) , order (exchange) , discrete mathematics , combinatorics , pure mathematics , algebra over a field , physics , motion (physics) , finance , economics , classical mechanics
The logics L 1 ( Q ), L 1,1 ( Q ) and L 2 ( Q ) are formed by adding quantifiers Q , Q 1,1 and Q 2 respectively to the first‐order logic. In this paper, for each ordinal α (including α = 0), we construct two Q α models to prove that the Interpolation Theorem fails in L ( Q ) and L 1,1 ( Q ).