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- W1976500787 abstract "We show in this paper that the theory of ordinal addition of any fixed ordinal ω α , with α less than ω ω , admits a quantifier elimination. This in particular gives a new proof for the decidability result first established in 1965 by R. Büchi using transfinite automata. Our proof is based on the Ehrenfeucht games, and we show that quantifier elimination go through generalized power. On montre ici que, pour tout ordinal α inférieur à ω ω , la théorie additive de ω α admet une élimination des quantificateurs. On obtient ainsi une nouvelle preuve de la décidabilité de ces théories (résultat de R. Büchi de 1965, basé sur des automates transfinis). On utilise ici les jeux d'Ehrenfeucht, avec un formalisme à la Ferrante et Rackoff, et on montre que le fait d'admettre une élimination des quantificateurs se transmet par produit généralisé." @default.
- W1976500787 created "2016-06-24" @default.
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- W1976500787 date "1997-12-01" @default.
- W1976500787 modified "2023-09-30" @default.
- W1976500787 title "Ehrenfeucht games and ordinal addition" @default.
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- W1976500787 doi "https://doi.org/10.1016/s0168-0072(97)00005-5" @default.
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