Talk:Bashicu matrix system

is there proofs that this is stronger than any nth-order arithmetic? :V

Fluoroantimonic Acid (talk) 17:35, January 8, 2016 (UTC)


 * No. It is stronger than just a "special type of" nth-order logic. 🐟 Fish fish fish ... 🐠 22:56, January 8, 2016 (UTC)


 * And what is this "special type of" nth-order logic we talk about? LittlePeng9 (talk) 08:07, January 9, 2016 (UTC)


 * It is a written in the proof of calculation termination (it is written in special terminology and it is difficult to translate into English... I hope some Japanese can translate it into English). For example, calculation of 2-row matrix can be expressed with 2nd order logic. Bashicu matrix does not cover "all of" 2nd order logic (it means that it does not diagonize over the entire 2nd order logic), but special "kind" or "type" of 2nd order logic, as defined in the algorithm. 🐟 Fish fish fish ... 🐠 08:37, January 9, 2016 (UTC)


 * In the proof it is written "n行でn階述語論理のある体系（n階のカインド）を対角化した強さとなる. " Literally it says n-row matrix diagonizes a special type of n-th order logic (n-th order kind). I am not sure if the word "n-th order kind" is a familiar usage of terminology, but anyway in the proof the word "hight of kind" is used. 🐟 Fish fish fish ... 🐠 08:46, January 9, 2016 (UTC)


 * I posted the Japanese BBS for help. Let's wait if some Japanese googlogist who knows logic better than me can explain in more detail... 🐟 Fish fish fish ... 🐠 09:00, January 9, 2016 (UTC)


 * Now the one who posted the proof starts to write more detailed version of the proof. I am asking him or her to make English version of the proof. 🐟 Fish fish fish ... 🐠 17:05, January 10, 2016 (UTC)


 * ja:ユーザー:黒羽カフカ "バシク行列の計算可能性の証明はもうしばらくお待ちください. " means "Please wait for a while until I rewrite the proof of computability of Bashicu matrix" 🐟 Fish fish fish ... 🐠 17:02, January 18, 2016 (UTC)

In Rule 3-2, what are \(L\) and what is \(m\)? While editing I have added "by choice of \(L\)" as I believe that is the case, but I want that clarified. Also, how is \(\Delta\) ever used? It is defined in Rule 3-3, but doesn't appear elsewhere. LittlePeng9 (talk) 20:23, January 8, 2016 (UTC)
 * From the example, it appears that Rule 3-3 is meant to specify \(\Delta\), not \(N\). I'm assuming that this is correct, and changing it. ~εmli 22:37, January 8, 2016 (UTC)


 * Looks like \(L\) is \(S_1\). Deedlit11 (talk) 02:16, January 9, 2016 (UTC)
 * Also, \(m\) is the number of rows in the matrix, or in other words the length of each vector. Deedlit11 (talk) 02:22, January 9, 2016 (UTC)