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Relativized Grothendieck topoi
Annals of Pure and Applied Logic 161 (10):1299-1312 (2010)
Abstract
In this paper we define a notion of relativization for higher order logic. We then show that there is a higher order theory of Grothendieck topoi such that all Grothendieck topoi relativizes to all models of set theory with choiceMy notes
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Citations of this work
On Transferring Model Theoretic Theorems of $${\mathcal{L}_{{\infty},\omega}}$$ L ∞, ω in the Category of Sets to a Fixed Grothendieck Topos.Nathanael Leedom Ackerman - 2014 - Logica Universalis 8 (3-4):345-391.
Encoding Complete Metric Structures by Classical Structures.Nathanael Leedom Ackerman - 2020 - Logica Universalis 14 (4):421-459.
References found in this work
Admissible sets and structures: an approach to definability theory.Jon Barwise - 1975 - New York: Springer Verlag.
Relating First-Order Set Theories and Elementary Toposes.Steve Awodey & Thomas Streicher - 2007 - Bulletin of Symbolic Logic 13 (3):340-358.
Admissible Sets and Structures. An Approach to Definability Theory.Mark Nadel - 1978 - Journal of Symbolic Logic 43 (1):139-144.
Relating first-order set theories and elementary toposes.Steve Awodey, Carsten Butz & Alex Simpson - 2007 - Bulletin of Symbolic Logic 13 (3):340-358.
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