@Unpublished{     riba:hal-00776921,
  Author        = "Riba, Colin",
  Abstract      = "{We propose a forcing-based interpretation of monadic second-order logic (MSO) on omega-words in Weak MSO (WMSO). The interpretation is purely syntactic and compositional. We show that a formula with parameters is true in MSO if and only if its interpretation is true in WMSO. We also show that a closed formula is true in MSO if and only if its interpretation is provable under some axioms which hold for WMSO, but without axiomatizing it. We use model-theoretic arguments. Our approach is inspired from point-free topology: infinite words, seen a topological points, are approximated by filters of bounded segments. We devise forcing conditions such that the corresponding generic filters approximate Ramseyan factorizations of infinite words modulo satisfaction of formulas of a given quantifier depth. Our interpretation parallels some approaches to McNaughton's Theorem (equivalence between non-deterministic Buchi automata and deterministic Rabin automata) but the obtained formulas do not by themselves describe deterministic automata.}",
  affiliation   = "Laboratoire de l'Informatique du Parall{\'e}lisme - LIP",
  date-added    = "2013-07-09 13:05:12 +0000",
  date-modified = "2013-07-09 13:05:12 +0000",
  hal_id        = "hal-00776921",
  Keywords      = "Monadic Second Order Logic ; Forcing ; Buchi automata ; McNaughton Theorem ; Feferman-Vaught Composition Theorem ; Henkin Completeness",
  Language      = "Anglais",
  Month         = "January",
  PDF           = "http://hal.archives-ouvertes.fr/hal-00776921/PDF/main.pdf",
  Title         = "{Forcing MSO on Infinite Words in Weak MSO}",
  URL           = "http://hal.archives-ouvertes.fr/hal-00776921",
  Year          = "2013",
  bdsk-url-1    = "http://hal.archives-ouvertes.fr/hal-00776921",
  File          = "Forcing MSO on Infinite Words in Weak MSO - Riba (1) (0) - a - a - j.pdf",
  file-2        = "Forcing MSO on Infinite Words in Weak MSO - Riba (0) (1) - a - a - j.pdf"
}

@Unpublished{ riba:hal-00776921, Author = "Riba, Colin", Abstract = "{We propose a forcing-based interpretation of monadic second-order logic (MSO) on omega-words in Weak MSO (WMSO). The interpretation is purely syntactic and compositional. We show that a formula with parameters is true in MSO if and only if its interpretation is true in WMSO. We also show that a closed formula is true in MSO if and only if its interpretation is provable under some axioms which hold for WMSO, but without axiomatizing it. We use model-theoretic arguments. Our approach is inspired from point-free topology: infinite words, seen a topological points, are approximated by filters of bounded segments. We devise forcing conditions such that the corresponding generic filters approximate Ramseyan factorizations of infinite words modulo satisfaction of formulas of a given quantifier depth. Our interpretation parallels some approaches to McNaughton's Theorem (equivalence between non-deterministic Buchi automata and deterministic Rabin automata) but the obtained formulas do not by themselves describe deterministic automata.}", affiliation = "Laboratoire de l'Informatique du Parall{\'e}lisme - LIP", date-added = "2013-07-09 13:05:12 +0000", date-modified = "2013-07-09 13:05:12 +0000", hal_id = "hal-00776921", Keywords = "Monadic Second Order Logic ; Forcing ; Buchi automata ; McNaughton Theorem ; Feferman-Vaught Composition Theorem ; Henkin Completeness", Language = "Anglais", Month = "January", PDF = "http://hal.archives-ouvertes.fr/hal-00776921/PDF/main.pdf", Title = "{Forcing MSO on Infinite Words in Weak MSO}", URL = "http://hal.archives-ouvertes.fr/hal-00776921", Year = "2013", bdsk-url-1 = "http://hal.archives-ouvertes.fr/hal-00776921", File = "Forcing MSO on Infinite Words in Weak MSO - Riba (1) (0) - a - a - j.pdf", file-2 = "Forcing MSO on Infinite Words in Weak MSO - Riba (0) (1) - a - a - j.pdf" }