Provident sets and rudimentary set forcing

• Autorzy: A. R. D. Mathias
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03D65: Higher-type and set recursion theory
• 03E30: Axiomatics of classical set theory and its fragments
• 03E40: Other aspects of forcing and Boolean-valued models
• 03E45: Inner models, including constructibility, ordinal definability, and core models

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 230
• Numer: 2
• Strony: 99-148

Daty

wydano

2015

Twórcy

autor

A. R. D. Mathias

• Professeur émérite, ERMIT, Université de la Réunion
• Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Abt. f. Mathematische Logik, Eckerstrasse 1, D-79104 Freiburg, Germany

Identyfikatory

DOI

10.4064/fm230-2-1