matematisk logikk
Lagt inn: 11/10-2015 13:49
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Let 0 be a constant, let v and h be a unary function symbols, and let be a binary function symbol. Let l be the first-order language (0,v,h,f) and T be the L-theory consisting of the following non-logical axions:
(T1) v(0)=0
(T2) h(0)=0
(T3) (\forall[/x](\forall[/y](v(f(x,y)) = x)
(T4) ((\forall[/x](\forall[/y](h(f(x,y))=y)
Next, we give an ij´nductive definition of the prime terms:
- 0 is a prime term
- f(t1,t2) is a prime term if t1 and t2 are prime terms.
Theorem: For eachvariable-free L-terms t, there exists a prime term p such that T "grin" t = p.
Prove the theorem.
Let 0 be a constant, let v and h be a unary function symbols, and let be a binary function symbol. Let l be the first-order language (0,v,h,f) and T be the L-theory consisting of the following non-logical axions:
(T1) v(0)=0
(T2) h(0)=0
(T3) (\forall[/x](\forall[/y](v(f(x,y)) = x)
(T4) ((\forall[/x](\forall[/y](h(f(x,y))=y)
Next, we give an ij´nductive definition of the prime terms:
- 0 is a prime term
- f(t1,t2) is a prime term if t1 and t2 are prime terms.
Theorem: For eachvariable-free L-terms t, there exists a prime term p such that T "grin" t = p.
Prove the theorem.