Isabelle/HOL-NSA — Non-Standard Analysis

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2 Filter: Filters and Ultrafilters 13 2.1 Definitions and basic properties . . . . . . . . . . . . . . . . . 13 2.1.1 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.2 Ultrafilters . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.3 Free Ultrafilters . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Collect properties . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Maximal filter = Ultrafilter . . . . . . . . . . . . . . . . . . . 15 2.4 Ultrafilter Theorem . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Unions of chains of superfrechets . . . . . . . . . . . . 16 2.4.2 Existence of free ultrafilter . . . . . . . . . . . . . . . 17

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Isabelle/HOL-NSA — Non-Standard Analysis

3 Construction of Star Types Using Ultrafilters 14 3.1 A Free Ultrafilter over the Naturals . . . . . . . . . . . . . . . 15 3.2 Definition of star type constructor . . . . . . . . . . . . . . . 15 3.3 Transfer principle . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Standard elements . . . . . . . . . . . . . . . . . . . . . . . . 17 3.5 Internal functions . . . . . . . . . . . . . ....

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An Interpretation of Isabelle/HOL in HOL Light

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Importing HOL into Isabelle/HOL

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Bounded Model Generation for Isabelle/HOL

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