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Given two infinite sets X $X$ and I, $I$, and a filter {\cal F} ${\cal F}$ on I, $I$, one defines as usual the equivalence relation \approx_{\cal F} $\approx_{\cal F}$ on X^I $X^I$ and obtains the reduced power $Y = X^I / \approx_{\cal F}F}$. Question 1 : to what extent do such reduced powers differ when one filter on I $I$ is changed to another filter on I $I$ ? Question 2 : consider question 1 in the case of different ultrafilters on I, $I$, thus in the case of ultrapowers. |
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How much are reduced powers different ?Given two infinite sets X and I, and a filter {\cal F} on I, one defines as usual the equivalence relation \approx_{\cal F} on X^I and obtains the reduced power Y = X^I / \approx_{\cal F}. Question 1 : to what extent do such reduced powers differ when one filter on I is changed to another filter on I ? Question 2 : consider question 1 in the case of different ultrafilters on I, thus in the case of ultrapowers.
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