Tuesday, July 18 2000
Atomic sentences are formed by putting a predicate of aritiy n in front of n names (enclosed in parentheses and separated by commas). Atomic sentences are built from the identity predicate, =, using infix notation: the arguments are placed on either side of the predicate. (FOL, page 13).
No, (1+(1+1)) or ((1+1)+1) would be terms. (FOL, page20).
From the assumption `not A' and the derivation of a contradiction you
infer `A'. (Lecture 7/12/00)
From the assumption `not A' and the derivation of a contradiction you infer `A'. (Lecture 7/12/00)
An axiom system is inconsistent if it is possible to prove both a statement and its negation from the axioms. A system is consistent if it is not inconsistent. (Lecture 7/17/00)
An axiom $A$ is independent if it cannot be proved from the remaining axioms. An axiom system is independent, if all its axioms are independent from each other. (Lecture 7/17/00)