On a forcing model for non-standard arithmetic
On a forcing model for non-standard arithmetic
On a forcing model for non-standard arithmetic
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Sheaf semantics A <strong>non</strong>-principal ultrafilter A <strong><strong>for</strong>cing</strong> <strong>model</strong> <strong>for</strong> <strong>non</strong>-<strong>standard</strong> <strong>arithmetic</strong> Open questions<br />
Being <strong>standard</strong><br />
The <strong>model</strong> believes that a function f : N → N represents a<br />
<strong>standard</strong> natural number, if it is “locally constant”. More precisely:<br />
p −st(f ) ⇔ f ↾ p is bounded.<br />
In short, we end up with the <strong>model</strong> introduced by Avigad in:<br />
J. Avigad – Weak theories of <strong>non</strong><strong>standard</strong> <strong>arithmetic</strong> and analysis,<br />
in: Reverse mathematics 2001, Lect. Notes Log. 21, pp. 19–46.<br />
Benno van den Berg, TU Darmstadt, Germany <strong>On</strong> a <strong><strong>for</strong>cing</strong> <strong>model</strong> <strong>for</strong> <strong>non</strong>-<strong>standard</strong> <strong>arithmetic</strong>
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