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- W2026759926 abstract "The following inequalities between transfinite large inductive dimensions modulo absolutely additive (resp. multiplicative) Borel classes $A(alpha)$ (resp. $M(alpha))$ = begin{equation*} (i) ; ; ; A(0) mathsf{-trInd} geq M(0) mathsf{-trInd} geq max{A(1) mathsf{-trInd}, M(1) mathsf{-trInd}}, and (ii) ; ; ; min {A(alpha) mathsf{-trInd},M(alpha) mathsf{-trInd}} geq max {A(beta) mathsf{-trInd},M(beta) mathsf{-trInd}}, mathsf{where ;} 1 leq alpha < beta < omega_1. end{equation*} We show that for any two functions $a$ and $m$ from the set of ordinals $Omega = { alpha : alpha < omega_1 }$ to the set ${ -1 } cup Omega cup { infty }$ such that begin{equation*} (i) ; ; ; a(0) geq m(0) geq max{a(1),m(1)}, mathsf{and} (ii) ; ; ; min {a(alpha),m(alpha) } geq max { a(beta),m(beta)}, mathsf{whenever ;} 1 geq alpha < beta < omega_1, end{equation*} there is a separable metrizable space X such that $A(alpha) mathsf{-trInd}X = a(/alpha)$ and $M(alpha) mathsf{-trInd}X = m(alpha)$ for each $0 geq alpha < omega_1$." @default.
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- W2026759926 date "2009-02-01" @default.
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- W2026759926 title "Transfinite large inductive dimensions modulo absolute Borel classes" @default.
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- W2026759926 doi "https://doi.org/10.2969/jmsj/06120327" @default.
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