B. Courcelle and J.A. Makowsky. VR and HR graph grammars: A common algebraic framework compatible with monadic second order logic. In Graph transformations, 2000. cf. tfs.cs.tuberlin. de/gratra2000/proceedings.html.

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Towards a language theory for infinite N-free pomsets - Kuske (2000)   (Correct)

....are special cases of the generalized sum as considered by Shelah [She75] The preceding theorem follows from his result [She75, Thm. 2.4] A condensed proof of Shelah s result can be found in [Gur79] for lexicographic sums of linear orders, Tho97] contains the full proof. In the terminology of [CM00] the first statements say that the sequential and the parallel product are Hintikka operations. These results can also be derived from [CM00] on quantifier free definable operations. Shelah is also interested in the effective computability of the combined theory from the argument theories. If ....

....condensed proof of Shelah s result can be found in [Gur79] for lexicographic sums of linear orders, Tho97] contains the full proof. In the terminology of [CM00] the first statements say that the sequential and the parallel product are Hintikka operations. These results can also be derived from [CM00] on quantifier free definable operations. Shelah is also interested in the effective computability of the combined theory from the argument theories. If one is only interested in the result as stated above, an alternative and much simpler proof of both statements can be given using ....

B. Courcelle and J.A. Makowsky. VR and HR graph grammars: A common algebraic framework compatible with monadic second order logic. In Graph transformations, 2000. cf. tfs.cs.tuberlin. de/gratra2000/proceedings.html.

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