Geodesic
Reductions between meager ideals
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 213-219

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We construct a nonmeager ideal, which is not a P-ideal yet $\mathrm{Fin}\times\varnothing$ is not reducible to it. 
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     author = {I. Farah},
     title = {Reductions between meager ideals},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     volume = {11},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a16/}
}
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I. Farah. Reductions between meager ideals. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 213-219. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a16/