Structure( Cont Definition A structure A for a language l consists of nonempty domain A o an assignment to each n-ary predicate symbol r of C,of an actual predicate R a on the n-tuples from A O an assignment, to each constant symbol c of L, of an element cA of A and, to each n-ary function symbol f of L
Structure(Cont.) . Definition . . A structure A for a language L consists of 1. a nonempty domain A, 2. an assignment, to each n-ary predicate symbol R of L, of an actual predicate R A on the n-tuples (a1, a2, . . . , an) from A, 3. an assignment, to each constant symbol c of L, of an element c A of A and, to each n-ary function symbol f of L, 4. an n-ary function f A from A n to A. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 8 / 27
Structure( Cont Definition A structure A for a language l consists of nonempty domain A o an assignment to each n-ary predicate symbol r of C,of an actual predicate R a on the n-tuples from A O an assignment, to each constant symbol c of L, of an element cA of A and, to each n-ary function symbol f of L o an n-ary function fa from an to A
Structure(Cont.) . Definition . . A structure A for a language L consists of 1. a nonempty domain A, 2. an assignment, to each n-ary predicate symbol R of L, of an actual predicate R A on the n-tuples (a1, a2, . . . , an) from A, 3. an assignment, to each constant symbol c of L, of an element c A of A and, to each n-ary function symbol f of L, 4. an n-ary function f A from A n to A. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 8 / 27
Structure( Cont am e Now we have three structures of language P(x, y), f(x,y
Structure(Cont.) . Example . . Now we have three structures of language P(x, y), f (x, y): 1. N , ≤, f A(x, y) = x · y. 2. Q, <, f A(x, y) = x ÷ y. 3. Z, >, f A(x, y) = x − y. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 9 / 27
Structure( Cont am e Now we have three structures of language P(x, y), f(x, oN,≤,f4(x,y)=x·y
Structure(Cont.) . Example . . Now we have three structures of language P(x, y), f (x, y): 1. N , ≤, f A(x, y) = x · y. 2. Q, <, f A(x, y) = x ÷ y. 3. Z, >, f A(x, y) = x − y. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 9 / 27
Structure( Cont am e Now we have three structures of language P(x, y), f(x, oN,≤,f4(x,y)=xy f(x,y)=x÷y
Structure(Cont.) . Example . . Now we have three structures of language P(x, y), f (x, y): 1. N , ≤, f A(x, y) = x · y. 2. Q, <, f A(x, y) = x ÷ y. 3. Z, >, f A(x, y) = x − y. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 9 / 27