Languages, automata, and logic
Handbook of formal languages, vol. 3
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Theoretical Computer Science - Latin American theoretical informatics
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
The Non-deterministic Mostowski Hierarchy and Distance-Parity Automata
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
On Monadic theories of monadic predicates
Fields of logic and computation
Equivalence and inclusion problem for strongly unambiguous büchi automata
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
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We give a new proof showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata theory. We discuss some applications of the result concerning unambiguous tree automata and definability of winning strategies in infinite games. In a second part we strengthen the result of the non-existence of an MSO-definable well-founded order on the infinite binary tree by showing that every infinite binary tree with a well-founded order has an undecidable MSO-theory.