Decidability of a relation on Functional space!
Suppose I have this functional space $(D={ asearrow b; a in A , b in B}, leqslant)$ (partial order relation on step functions!),also suppose that relation $leqslant_1$ is decidable on $(A,leqslant_1)$ and relation $leqslant_2$ is decidable on$(B,leqslant_2)$.
My question is that, is there any theorem or lemma which can make any relation between decidability of relation on D with relations on A andor B?!
D is countable, same as for A and B.
We say $asearrow b leqslant csearrow d$ if and only if $forall x in { countable set}; a leqslant_1 x rightarrow c leqslant_1 x$ implies $b leqslant_2 d$
analysis logic computability decidability domain-theory
asked Dec 10 '18 at 3:02
Yuval
64
add a comment |
Suppose I have this functional space $(D={ asearrow b; a in A , b in B}, leqslant)$ (partial order relation on step functions!),also suppose that relation $leqslant_1$ is decidable on $(A,leqslant_1)$ and relation $leqslant_2$ is decidable on$(B,leqslant_2)$.
My question is that, is there any theorem or lemma which can make any relation between decidability of relation on D with relations on A andor B?!
D is countable, same as for A and B.
We say $asearrow b leqslant csearrow d$ if and only if $forall x in { countable set}; a leqslant_1 x rightarrow c leqslant_1 x$ implies $b leqslant_2 d$
analysis logic computability decidability domain-theory
asked Dec 10 '18 at 3:02
Yuval
64
add a comment |
Suppose I have this functional space $(D={ asearrow b; a in A , b in B}, leqslant)$ (partial order relation on step functions!),also suppose that relation $leqslant_1$ is decidable on $(A,leqslant_1)$ and relation $leqslant_2$ is decidable on$(B,leqslant_2)$.
My question is that, is there any theorem or lemma which can make any relation between decidability of relation on D with relations on A andor B?!
D is countable, same as for A and B.
We say $asearrow b leqslant csearrow d$ if and only if $forall x in { countable set}; a leqslant_1 x rightarrow c leqslant_1 x$ implies $b leqslant_2 d$
analysis logic computability decidability domain-theory
asked Dec 10 '18 at 3:02
Yuval
64
Suppose I have this functional space $(D={ asearrow b; a in A , b in B}, leqslant)$ (partial order relation on step functions!),also suppose that relation $leqslant_1$ is decidable on $(A,leqslant_1)$ and relation $leqslant_2$ is decidable on$(B,leqslant_2)$.
My question is that, is there any theorem or lemma which can make any relation between decidability of relation on D with relations on A andor B?!
D is countable, same as for A and B.
We say $asearrow b leqslant csearrow d$ if and only if $forall x in { countable set}; a leqslant_1 x rightarrow c leqslant_1 x$ implies $b leqslant_2 d$
analysis logic computability decidability domain-theory
analysis logic computability decidability domain-theory
asked Dec 10 '18 at 3:02
Yuval
64
asked Dec 10 '18 at 3:02
Yuval
64
edited Dec 10 '18 at 3:17
asked Dec 10 '18 at 3:02
Yuval
64
asked Dec 10 '18 at 3:02
Yuval
64
asked Dec 10 '18 at 3:02
Yuval
64
64
add a comment |
add a comment |
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