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On a Spector Ultrapower for the Solovay Model
Author(s) -
Kanovei Vladimir,
van Lambalgen Michiel
Publication year - 1997
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.19970430311
Subject(s) - ultraproduct , mathematics , extension (predicate logic) , countable set , uniformization (probability theory) , set (abstract data type) , tree (set theory) , ultrafilter , discrete mathematics , combinatorics , statistics , computer science , balance equation , markov model , markov chain , programming language
We prove that a Spector‐like ultrapower extension of a countable Solovay model (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension [ a ], where a is a random real over . The proof involves the Solovay almost everywhere uniformization technique.