GlaR, T., Rathjen, M. and Schliiter, A., On the proof-theoretic

Annals of Pure and Applied Logic 85 (1):283 (1997)
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Ultrasheaves and Double Negation.Jonas Eliasson & Steve Awodey - 2004 - Notre Dame Journal of Formal Logic 45 (4):235-245.
Maharam spectra of Loeb spaces.Renling Jin & H. Jerome Keisler - 2000 - Journal of Symbolic Logic 65 (2):550-566.

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A model for intuitionistic non-standard arithmetic.Ieke Moerdijk - 1995 - Annals of Pure and Applied Logic 73 (1):37-51.
Minimal models of Heyting arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.
A constructive approach to nonstandard analysis.Erik Palmgren - 1995 - Annals of Pure and Applied Logic 73 (3):297-325.

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