Categories
Math

Non-Standard Axioms for Various Math Structures 9

In this post, we summarize my previous work of the series in a more readable and concise manner. (Proofs are not included.)

Categories
Math

Non-Standard Axioms for Various Math Structures 8

In this post, we continue the discussion from the previous in the series.

Categories
Math

Non-Standard Axioms for Various Math Structures 7

We continue the discussion from the previous post in the series.

Categories
Math

Non-Standard Axioms for Various Math Structures 6

We continue the discussion from this post.

Categories
Math

Non-Standard Axioms for Various Math Structures 5

In this post, we continue the discussion from the previous in the series.

Categories
Math

Non-Standard Axioms for Various Math Structures 4

We continue the discussion from the previous post in the series.

Categories
Math

Non-Standard Axioms for Various Math Structures 3

In this post, we continue the discussion from the previous in the series.

Categories
Math

Non-Standard Axioms for Various Math Structures 2

This is part of a series in which we investigate non-standard axiomatizations of various math structures. The previous post in the series was concerned with single equational axioms for equational classes. In this post, we are inspired by a particularly elegant characterization of (abstract) Boolean algebras, and we consider whether similar “Boolean algebra-like” characterizations can be given for other common structures.

Categories
Math

Non-Standard Axioms for Various Math Structures

This is the first post in a series. This started as an investigation of various non-standard axiomatizations of common structures, but soon the posts ended up focusing on a particular such kind of axiomatization. Thus, this title is misleading (and anyway, it seems too broad for a single series.)