fixed broken links to Wikipedia; replaced current links with permalinks where quotations are used, in case the quotes are removed in later versions

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edit approved Feb 9 at 15:13

The Amplitwist

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From wikipedia, we have definition of magma magma:

"InIn abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set M equipped with a single binary operation M × M → M. A binary operation is closed by definition, but no other axioms are imposed on the operation."

Axioms of magma structure are first order theory first order theory. So lets drop words "set" and "closed" from the definition, and try playing with theory T for which we have:

From Wikipedia article about First Order Logic First Order Logic I know that "hethe definition above requires that the domain of discourse of any interpretation must be a nonempty set." but it is a remark pointing to "empty domains empty domains" and "free logic free logic" which obviously are not in case here. The only interesting link is this: Interpretation_(model theory)Interpretation_(model theory) but it still is related to set or empty domain interpretations. But from category theory it seems to be possible to have theories which are interpreted in larger domains that sets in consistent way.

I would like to mention other questions in this or similar area here on mathoverflow, but I would like to say that I am not interested in category theory by other means than just an example of theory which is has other domain of interpretation than set.:
Is there a relationship between model theory and category theory?
Categorical foundations without set theory

From wikipedia, we have definition of magma:

"In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set M equipped with a single binary operation M × M → M. A binary operation is closed by definition, but no other axioms are imposed on the operation."

Axioms of magma structure are first order theory. So lets drop words "set" and "closed" from the definition, and try playing with theory T for which we have:

From Wikipedia article about First Order Logic I know that "he definition above requires that the domain of discourse of any interpretation must be a nonempty set." but it is a remark pointing to "empty domains" and "free logic" which obviously are not in case here. The only interesting link is this: Interpretation_(model theory) but it still is related to set or empty domain interpretations. But from category theory it seems to be possible to have theories which are interpreted in larger domains that sets in consistent way.

I would like to mention other questions in this or similar area here on mathoverflow, but I would like to say that I am not interested in category theory by other means than just an example of theory which is has other domain of interpretation than set.: Is there a relationship between model theory and category theory? Categorical foundations without set theory

From wikipedia, we have definition of magma:

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set M equipped with a single binary operation M × M → M. A binary operation is closed by definition, but no other axioms are imposed on the operation.

Axioms of magma structure are first order theory. So lets drop words "set" and "closed" from the definition, and try playing with theory T for which we have:

From Wikipedia article about First Order Logic I know that "the definition above requires that the domain of discourse of any interpretation must be a nonempty set." but it is a remark pointing to "empty domains" and "free logic" which obviously are not in case here. The only interesting link is this: Interpretation_(model theory) but it still is related to set or empty domain interpretations. But from category theory it seems to be possible to have theories which are interpreted in larger domains that sets in consistent way.

I would like to mention other questions in this or similar area here on mathoverflow, but I would like to say that I am not interested in category theory by other means than just an example of theory which is has other domain of interpretation than set.:
Is there a relationship between model theory and category theory?
Categorical foundations without set theory

replaced http://mathoverflow.net/ with https://mathoverflow.net/

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edited Apr 13, 2017 at 12:57

Community Bot

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Following the blow blow. I will try to ask question in order to check if I well understand what was pointed. I decide to ask another question, because mathoverflow is not projected to be good environment for discussion, so it would be better to ask another question than to modify previous one.

I would like to mention other questions in this or similar area here on mathoverflow, but I would like to say that I am not interested in category theory by other means than just an example of theory which is has other domain of interpretation than set.: Is there a relationship between model theory and category theory?Is there a relationship between model theory and category theory? Categorical foundations without set theory Categorical foundations without set theory