Choice functions and well-orderings over the infinite binary tree

• Autorzy: Arnaud Carayol , Christof Löding , Damian Niwinski , Igor Walukiewicz
• Języki publikacji: EN

Abstrakty

EN

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 show how the result can be used to prove the inherent ambiguity of languages of infinite trees. 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.

Słowa kluczowe

EN

Monadic second-order logic; Definability; Choice function

Kategorie tematyczne

• 03B70: Logic in computer science

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 4
• Strony: 662-682

Daty

wydano

2010-08-01

online

2010-07-24

Twórcy

autor

Arnaud Carayol

• Laboratoire d’Informatique Gaspard Monge, Université Paris-Est, Paris, France

autor

Christof Löding

• Lehrstuhl Informatik 7, RWTH Aachen, Aachen, Germany

autor

Damian Niwinski

• Institute of Informatics, University of Warsaw, Warsaw, Poland

autor

Igor Walukiewicz

• LaBRI, Bordeaux University & CNRS, Bordeaux, France

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Identyfikatory

DOI

10.2478/s11533-010-0046-z