This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CS245  Winter 2010, Lecture of Feb. 26th Shai BenDavid In this lecture we discuss definability for first order logic (FOL). There two different notions of definability. 0.1 Definability of a set of structures Definition Let L be a language. A set of Lstructure, K is (strongly) definable if there exists a FOL formula in this language such that K = { M : M  = } . In that case, we say that defines K . Examples: 1. Let L = . (a) K 2 def = { M :  U M  2 } (where U M denotes the universe of the structure M ) is definable by the formula x y z ( x = y x = z y = z ). (b) K 2 def = { M :  U M  2 } is definable by the formula x y ( x 6 = y ). 2. Let L = h R ( , ) i where R is a twoplace relation symbol. (a) Let K equiv def = { M : R M is an equivalence relation } (recall that an equivalence relation is a relation that is symmetric, transitive and reflexive). Then K equiv is defined by ( 1 2 3 ), where...
View Full
Document
 Spring '08
 A

Click to edit the document details