Reference on many-sorted logic
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I am starting to read category theory and I would like to learn, for example, 2-sorted logic necessary to axiomatize category theory.
As a background, I have read Kleene's "Introduction to Metamathematics". I would appreciate any recommendation/reference for learning many-sorted logic. It would be preferable if the overall style is similar to Kleene's (if you are familiar with it). I would also like to have many sorted logic be developed in weak metatheory like PRA, instead of ZFC or other forms of set theory.
logic
asked Nov 15 at 3:31
Daniels Krimans
45928
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I am starting to read category theory and I would like to learn, for example, 2-sorted logic necessary to axiomatize category theory.
As a background, I have read Kleene's "Introduction to Metamathematics". I would appreciate any recommendation/reference for learning many-sorted logic. It would be preferable if the overall style is similar to Kleene's (if you are familiar with it). I would also like to have many sorted logic be developed in weak metatheory like PRA, instead of ZFC or other forms of set theory.
logic
asked Nov 15 at 3:31
Daniels Krimans
45928
1
$2$-sorted logic isn't necessary to axiomatize category theory: you can do everything in terms of arrows only, thinking of objects as being represented by identity morphisms. And generally, many-sorted logic with finitely many sorts can be translated directly into first-order logic by replacing each sort with a unary predicate.
– Noah Schweber
Nov 17 at 14:13
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am starting to read category theory and I would like to learn, for example, 2-sorted logic necessary to axiomatize category theory.
As a background, I have read Kleene's "Introduction to Metamathematics". I would appreciate any recommendation/reference for learning many-sorted logic. It would be preferable if the overall style is similar to Kleene's (if you are familiar with it). I would also like to have many sorted logic be developed in weak metatheory like PRA, instead of ZFC or other forms of set theory.
logic
asked Nov 15 at 3:31
Daniels Krimans
45928
I am starting to read category theory and I would like to learn, for example, 2-sorted logic necessary to axiomatize category theory.
As a background, I have read Kleene's "Introduction to Metamathematics". I would appreciate any recommendation/reference for learning many-sorted logic. It would be preferable if the overall style is similar to Kleene's (if you are familiar with it). I would also like to have many sorted logic be developed in weak metatheory like PRA, instead of ZFC or other forms of set theory.
logic
logic
asked Nov 15 at 3:31
Daniels Krimans
45928
asked Nov 15 at 3:31
Daniels Krimans
45928
asked Nov 15 at 3:31
Daniels Krimans
45928
asked Nov 15 at 3:31
Daniels Krimans
45928
asked Nov 15 at 3:31
Daniels Krimans
45928
45928
1
$2$-sorted logic isn't necessary to axiomatize category theory: you can do everything in terms of arrows only, thinking of objects as being represented by identity morphisms. And generally, many-sorted logic with finitely many sorts can be translated directly into first-order logic by replacing each sort with a unary predicate.
– Noah Schweber
Nov 17 at 14:13
add a comment |
1
$2$-sorted logic isn't necessary to axiomatize category theory: you can do everything in terms of arrows only, thinking of objects as being represented by identity morphisms. And generally, many-sorted logic with finitely many sorts can be translated directly into first-order logic by replacing each sort with a unary predicate.
– Noah Schweber
Nov 17 at 14:13
1
1
$2$-sorted logic isn't necessary to axiomatize category theory: you can do everything in terms of arrows only, thinking of objects as being represented by identity morphisms. And generally, many-sorted logic with finitely many sorts can be translated directly into first-order logic by replacing each sort with a unary predicate.
– Noah Schweber
Nov 17 at 14:13
$2$-sorted logic isn't necessary to axiomatize category theory: you can do everything in terms of arrows only, thinking of objects as being represented by identity morphisms. And generally, many-sorted logic with finitely many sorts can be translated directly into first-order logic by replacing each sort with a unary predicate.
– Noah Schweber
Nov 17 at 14:13
add a comment |
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$2$-sorted logic isn't necessary to axiomatize category theory: you can do everything in terms of arrows only, thinking of objects as being represented by identity morphisms. And generally, many-sorted logic with finitely many sorts can be translated directly into first-order logic by replacing each sort with a unary predicate.
– Noah Schweber
Nov 17 at 14:13