On the connection between nonstandard analysis and constructive analysis

Sam Sanders

Abstract



Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Ω-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren’s development of Nonstandard Analysis inside constructive mathematics.

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