wiki_research

commit 5bcd0e7a21a6454452ab535c1a81ac8180ec2bfb
parent 9000341fa710c499c6a259d01742420374750e8c
Author: Antoine Amarilli <a3nm@a3nm.net>
Date:   Tue, 18 Feb 2025 17:50:45 +0100

commit with codex

Diffstat:
logic
 | 
1
+
naturally_ordered_semiring
 | 
2
+-
semiring_idempotent
 | 
2
++
semiring_multiplicative_idempotent
 | 
7
+++++++
semiring_n_idempotent
 | 
7
+++++++

5 files changed, 18 insertions(+), 1 deletion(-)
diff --git a/logic b/logic
@@ -29,6 +29,7 @@
 
 - [finite_model_theory]
   - [finite_controllability]
+- [non_classical_logics]
 
 ## Tools
 
diff --git a/naturally_ordered_semiring b/naturally_ordered_semiring
@@ -4,4 +4,4 @@
 
 Up: [natural_order], [semiring]
 
-Aliases: naturally ordered semirings
+Aliases: naturally ordered semirings, semiring naturally ordered
diff --git a/semiring_idempotent b/semiring_idempotent
@@ -4,6 +4,8 @@ A [semiring] satisfying the equation a+a = a for every a ("additively idempotent
 
 Not the case of all [semirings], e.g., not the [natural_numbers]
 
+Also [semiring_multiplicative_idempotent]
+
 Up: [semiring], [idempotent]
 
 Aliases: semiring idempotence, idempotent semiring, idempotent semirings
diff --git a/semiring_multiplicative_idempotent b/semiring_multiplicative_idempotent
@@ -0,0 +1,7 @@
+# Semiring multiplicative idempotent
+
+[Semiring] where s s = s for all s
+
+Generalization: [semiring_n_idempotent]
+
+Up: [semiring_idempotent]
diff --git a/semiring_n_idempotent b/semiring_n_idempotent
@@ -0,0 +1,7 @@
+# Semiring n idempotent
+
+[Semiring] where s^n s = s^n
+
+Special case: [semiring_multiplicative_idempotent]
+
+Up: [semiring]