Premium
Decidability and Definability Results Concerning Well‐Orderings and Some Extensions of First Order Logic
Author(s) -
Chlebus Bogdan Stanislaw
Publication year - 1980
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19800263402
Subject(s) - decidability , order (exchange) , citation , computer science , algebra over a field , mathematics , algorithm , library science , pure mathematics , finance , economics
This quantifier binds one variable in each formula of the pair of formulas. L”(“) for a natural n or n = co denotes the (first order) expansion of L obtained by adding to L two predicate symbols 7 and E. By a structure appropriate for L‘(“) is meant any structure = (A“, . . .) defined as follows : 1) ?( = ( A , , . . .) is a structure appropriate for L in the ordinary sense, 2) for a natural n, the universe of %@+l) is the set A,,+1 = {x: z E A,, or x is a finite subset of A,)} and A , = U A f , . new 3) &P) k ~ ( a ) iff a E A , (for a E A,,) .