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Ashutosh
Ashutosh
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Let I denote the null (repsresp. meager) ideal on reals. Is it consistent that for any pair of non null (resp. meager) sets A and B, there is a null (resp. meager) preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen (resp. random reals) over a model of CH?

Let I denote the null (reps. meager) ideal on reals. Is it consistent that for any pair of non null (resp. meager) sets A and B, there is a null (resp. meager) preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen (resp. random reals) over a model of CH?

Let I denote the null (resp. meager) ideal on reals. Is it consistent that for any pair of non null (resp. meager) sets A and B, there is a null (resp. meager) preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen (resp. random reals) over a model of CH?

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Ashutosh
Ashutosh
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Let I denote the null/meager (reps. meager) ideal on reals. Is it consistent that for any pair of non null/meager (resp. meager) sets A and B, there is a null/meager (resp. meager) preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen/random (resp. random reals) over a model of CH?

Let I denote the null/meager ideal on reals. Is it consistent that for any pair of non null/meager sets A and B, there is a null/meager preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen/random reals over a model of CH?

Let I denote the null (reps. meager) ideal on reals. Is it consistent that for any pair of non null (resp. meager) sets A and B, there is a null (resp. meager) preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen (resp. random reals) over a model of CH?

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Ashutosh
Ashutosh
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Restrictions of null/meager ideal

Let I denote the null/meager ideal on reals. Is it consistent that for any pair of non null/meager sets A and B, there is a null/meager preserving bijection between A and B? In particular, is this true in the model obtained by adding $\omega_2$ Cohen/random reals over a model of CH?