@inproceedings{10.1007/978-3-540-30124-0_7,
    Abstract = {The logic MSOL+ {\$}{\backslash}mathbb{\{}B{\}}{\$} is defined, by extending monadic second-order logic on the infinite binary tree with a new bounding quantifier {\$}{\backslash}mathbb{\{}B{\}}{\$} . In this logic, a formula {\$}{\backslash}mathbb{\{}B{\}}{\$} X. $\phi$(X) states that there is a finite bound on the size of sets satisfying $\phi$(X). Satisfiability is proved decidable for two fragments of MSOL+ {\$}{\backslash}mathbb{\{}B{\}}{\$} : formulas of the form {\$}{\backslash}neg{\backslash}mathbb{\{}B{\}}{\$} X.$\phi$(X), with $\phi$ a {\$}{\backslash}mathbb{\{}B{\}}{\$} -free formula; and formulas built from {\$}{\backslash}mathbb{\{}B{\}}{\$} -free formulas by nesting {\$}{\backslash}mathbb{\{}B{\}}{\$} , ∃, ∨ and ∧.},
    Address = {Berlin, Heidelberg},
    Author = {Boja{\'{n}}czyk, Miko{{\l}}aj},
    BookTitle = {Computer Science Logic},
    Editor = {Marcinkowski, Jerzy and Tarlecki, Andrzej},
    File = {../.Trash/confcslBojanczyk04 (0).pdf},
    ISBN = {978-3-540-30124-0},
    Pages = {41--55},
    Publisher = {Springer Berlin Heidelberg},
    Title = {A Bounding Quantifier},
    Year = {2004},
    date-added = {2018-07-16 21:26:36 +0000},
    date-modified = {2018-07-16 21:26:36 +0000},
    doi = {10.1007/978-3-540-30124-0_7}
}

@inproceedings{10.1007/978-3-540-30124-0_7, Abstract = {The logic MSOL+ {\$}{\backslash}mathbb{{}B{}}{\$} is defined, by extending monadic second-order logic on the infinite binary tree with a new bounding quantifier {\$}{\backslash}mathbb{{}B{}}{\$} . In this logic, a formula {\$}{\backslash}mathbb{{}B{}}{\$} X. $\phi$(X) states that there is a finite bound on the size of sets satisfying $\phi$(X). Satisfiability is proved decidable for two fragments of MSOL+ {\$}{\backslash}mathbb{{}B{}}{\$} : formulas of the form {\$}{\backslash}neg{\backslash}mathbb{{}B{}}{\$} X.$\phi$(X), with $\phi$ a {\$}{\backslash}mathbb{{}B{}}{\$} -free formula; and formulas built from {\$}{\backslash}mathbb{{}B{}}{\$} -free formulas by nesting {\$}{\backslash}mathbb{{}B{}}{\$} , ∃, ∨ and ∧.}, Address = {Berlin, Heidelberg}, Author = {Boja{\'{n}}czyk, Miko{{\l}}aj}, BookTitle = {Computer Science Logic}, Editor = {Marcinkowski, Jerzy and Tarlecki, Andrzej}, File = {../.Trash/confcslBojanczyk04 (0).pdf}, ISBN = {978-3-540-30124-0}, Pages = {41--55}, Publisher = {Springer Berlin Heidelberg}, Title = {A Bounding Quantifier}, Year = {2004}, date-added = {2018-07-16 21:26:36 +0000}, date-modified = {2018-07-16 21:26:36 +0000}, doi = {10.1007/978-3-540-30124-0_7} }