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- W2065894311 abstract "We introduce a version of operational set theory, OST − , without a choice operation, which has a machinery for Δ 0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST , based on Gödel operations. We show that both the theories and Kripke–Platek set theory KP with infinity are pairwise Π 1 equivalent. We also show analogous assertions for subtheories with ∈-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KP , the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model." @default.
- W2065894311 created "2016-06-24" @default.
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- W2065894311 date "2015-02-01" @default.
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- W2065894311 title "A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msub><mml:mrow><mml:mi>Π</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-equivalent to KP" @default.
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