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 />
Intuitionistic <strong>model</strong> 1<br />
We work in PSh(P). This means: <strong><strong>for</strong>cing</strong> clauses <strong>for</strong> the atomic<br />
<strong>for</strong>mulas as above and the clauses <strong>for</strong> the interpretation of logical<br />
connectives as in Kripke semantics.<br />
Interesting fact:<br />
Lemma<br />
In PSh(P) the double negation shift holds:<br />
PSh(P) |= ∀n ∈ N(¬¬P(n)) → ¬¬∀nP(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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