Titlebook: Logic and Games on Automatic Structures; Playing with Quantif Łukasz Kaiser Book 2011 Springer-Verlag GmbH Berlin Heidelberg 2011 Game theo

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Cardinality Quantifiers in MSO on Trees,In this chapter, we extend the results on second-order cardinality quantifiers, shown for linear orders in the previous chapter, to trees. Our main result, obtained together with Vince Bárány and Alexander Rabinovich [8,9], is that the uncountability quantifier can be eliminated from . over trees.

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Cardinality Quantifiers in MSO on Linear Orders,ch we introduced in section 1.5 as the ones that are .-to-. interpretable in a tree. It is therefore a natural extension of the previous work to ask whether counting quantifiers preserve regularity on such generalized-automatic structures.

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0302-9743 automatic structures are in fact finite-word automatic and that the infinity and uncountability set quantifiers are defina978-3-642-22806-3978-3-642-22807-0Series ISSN 0302-9743 Series E-ISSN 1611-3349

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