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Truth in all of certain well‐founded countable models arising in set theory
Author(s) -
Rosenthal John W.
Publication year - 1975
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.19750210113
Subject(s) - countable set , set (abstract data type) , citation , computer science , mathematical economics , mathematics , discrete mathematics , library science , programming language
Let M be a countable, transitive, &-model of ZF, V = L, i.e.-one of the models used by COHEN et al. [4] as the “starting point’’ for their independence results in set theory. In this model ramified languages L(T) or L ( T i , i E I) are defined to describe fully the models M (T) or M ( T i , i E I) used in independence results. We study the question-is {c E r 1 M ( T ) I= 0, VTf M-definable where r is the formulae of a certain bounded complexity. We show if r is 6 U2-unranked formulae it is, but if r is i Cnunranked formulae it is not.