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 />
First useful fact<br />
Lemma<br />
The ordinary functions N → N lie dense in the object playing the<br />
rôle of N → N in E, and there<strong>for</strong>e validity of statements<br />
concerning N → N in E can be reduced to validity of statements<br />
concerning ordinary functions N → N.<br />
Proof.<br />
Use the key combinatorial lemma.<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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