2010_lecFeb26

# 2010_lecFeb26 - CS245 Winter 2010 Lecture of Feb 26th Shai...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS245 - Winter 2010, Lecture of Feb. 26th Shai Ben-David 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 L-structure, K is (strongly) definable if there exists a FOL formula in this language α such that K = { M : M | = α } . In that case, we say that α 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 two-place 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 α ≡ ( β 1 ∧ β 2 ∧ β 3 ), where • β...
View Full Document

## This note was uploaded on 04/07/2010 for the course CS 245 taught by Professor A during the Spring '08 term at Waterloo.

### Page1 / 2

2010_lecFeb26 - CS245 Winter 2010 Lecture of Feb 26th Shai...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online