Titlebook: Logic and Games on Automatic Structures; Playing with Quantif ?ukasz 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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ngfügigen Vorteil absehen wollen, der sich einem Spieler dadurch bietet, da? einer den ersten Zug zu machen hat. Auf bestimmte Fragen, die ein Geschicklichkeitsspiel aufwirft, werden wir am Schlu? dieses Paragraphen noch kurz zu sprechen kommen In erster Linie sollen uns aber zun?chst einmal die rei

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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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