Hilbert Levitz

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This paper deals mainly with generalizations of results in nitary combinatorics to innnite ordinals. It is well-known that for nite ordinals P << is the number of 2-element subsets of an-element set. It is shown here that for any well-ordered set of arbitrary innnite order type , P << is the ordinal of the set M of 2-element subsets where M is ordered in(More)
and MATIJASEVI~: [6] characterizations of recursively enumerable sets. Our principal result is the following. To each f . 9 E Tktl t8here exists a function h E T , such that for each I* = (y, . yz . . . ~ y,) E N", if i lrf(r, Y ) + Arg(x, Y ) then h( F) bounds the real %roots (if any) of the equation f ( . r . Y ) = g ( s , IT). Surprisingly h can be taken(More)
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