We present in this paper an algebraic approach to the theory of languages of words on countable ordinals. The algebraic structure used, called an omiga-semigroup, is an adaptation of hte one used in the theroy of regular languages of omiga-words. We show that finite omiga sub 1-semigroups are equivalent to automata. In particular, the proof gives a new algorithm for determinizing automata on countable ordinals. As in the cases of finite and omiga-words, a syntactic omiga sub 1-semigroup can effectively be associated with any regular language of words on countable ordinals. This result is used to prove an Eilenberg type theorem. There is a one-to-one corespondence between varieties of omiga sub 1-languages and pseudo-varietie of omiga sub 1-semigroups.
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机译：我们在本文中提出了一种对可数序数词语言理论的代数方法。所使用的代数结构称为omiga-半群，是对omiga-word常规语言理论中使用的一种代数的改编。我们证明了有限的奥米加亚1-半群等价于自动机。特别是，证明给出了一种确定可数序数上自动机的新算法。与有限和奥米加语单词的情况一样，句法奥米加亚1-半群可以有效地与可数序数上的任何常规单词语言相关联。此结果用于证明Eilenberg型定理。 omiga sub 1语言的变体与omiga sub 1半族的伪变种之间存在一对一的对应关系。
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