have you ever met with notation of $P^+$-families in other papers than Iian B. Smythe "A local Ramsey theory for block sequences" and his phd? Thank you in advance
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$\begingroup$ $P^+$-filters are quite common in the literature. Can you provide the definition of a $P^+$-family? $\endgroup$– Damian SobotaCommented Mar 23, 2020 at 14:48
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$\begingroup$ Thank you for the answer. Up to my knowledge, a family $A$ is "standard" $P^+$ - family if each countable subset of $A$ has pseudointersection in $A^+$. But I'm looking for a non-standard understending of this notation. The reason is following: I've written a paper with the definition (in short): let us call {\it contur} first iteration of Fr\'{e}chet filter (by Frolik sum = tensor produkt =..) The family $A$ with fip {\it is not quasi finer than a contur} if for each countable family $B$, such that $A \cup B$ fas fip, there is no contur $C$ such that $\langle A \cup B \rangle \supset C$. $\endgroup$– Andrzej StarosolskiCommented Mar 24, 2020 at 9:24
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$\begingroup$ I've send a manuscript to IJM and the referee write, that this definition is well known as a $P^+$-family. Since obviousely those definition describes different classes of families, thus I'm looking "non-standard" definition of the $P^+$-family. By the way, if you would like to look at the paper an old version is on Arxive arxiv.org/pdf/1803.03862v3.pdf (with one incorectness and a different notation: for "is not quasi finer than a contur" is used "is not EQ-subbase of the contur"), a new wersion I'll add to Arxive soon. Best regards $\endgroup$– Andrzej StarosolskiCommented Mar 24, 2020 at 9:26
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