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Abstrakty
Using the theory of rudimentary recursion and provident sets expounded in [MB], we give a treatment of set forcing appropriate for working over models of a theory PROVI which may plausibly claim to be the weakest set theory supporting a smooth theory of set forcing, and of which the minimal model is Jensen's $J_ω$. Much of the development is rudimentary or at worst given by rudimentary recursions with parameter the notion of forcing under consideration. Our development eschews the power set axiom. We show that the forcing relation for Δ̇₀ wffs is propagated through our hierarchies by a rudimentary function, and we show that the construction of names for the values of rudimentary and rudimentarily recursive functions is similarly propagated. Our main result is that a set-generic extension of a provident set is provident.
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Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
99-148
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Professeur émérite, ERMIT, Université de la Réunion
- Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Abt. f. Mathematische Logik, Eckerstrasse 1, D-79104 Freiburg, Germany
Bibliografia
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-1