RAM et ultrafiltre

Title: Structures de réalisabilité, RAM et ultrafiltre sur N

Author: Jean-Louis Krivine

Abstract: We show how to transform into programs the proofs in classical Analysis which use the existence of an ultrafilter on the integers. The method mixes the classical realizability introduced by the author, with the “forcing” of P. Cohen. The programs we obtain, use read and write instructions in random access memory.

Illustrated guide to model theory: 2

(*) Every Man Needs A GOOD FORKING – Fridge Magnet

thank goodness

Shortly before the World War he [Zermelo] spent a night in the Bavarian alps. He filled the column “Nationality” in the hotel’s registration form with the words: “Not Swiss, thank goodness.”  Misfortune would have it that shortly after that the head of the Education Department of the Canton Zürich stayed at the same hotel and saw the entry. It was clear that Zermelo could not stay much longer at the University of Zürich.

(*) from Abraham Fraenkel’s “Lebenskrise”

Illustrated guide to model theory: 1

(*)  forkingfantastic.com

Topolozhstvo

in 1946, on the floor of the Academy of Sciences, Kolmogorov said something about his recent work on topology to Luzin, and the latter replied, “Eto ne topologiia, eto topolozhstvo” (“This is not topology, this is topolozhstvo“). Kolmogorov reddened and struck Luzin in the face. The word “topolozhstvo” is an invented term with a very clear meaning. In Russian the word skotolozhstvo means “bestiality,” while muzhelozhstvo means “sodomy.” Therefore, “topolozhstvo” was a word contrived by Luzin that might be translated as “topological pederasty.”

(*)

From “Naming Infinity” by Loren Graham and Jean-Michel Kantor

An interesting temporalization

Title: An interesting temporalization of Godel’s ontological proof;

Author: Gavriel Segre

Recent theologies concerning God’s death after Auschwitz are mathematically formalized through a suitable temporalization of Goedel’s Ontological Proof.

Identity of indiscernibles

“Just take an ultrafilter D”
Saharon Shelah

“God is the Alexandroff compactification of the Universe”
Alexander Grothendieck

“Stone-Cech compactification of the Universe is the paganic polytheism”
Folklore

(*)

Goedel’s formalization of ontological argument using ultrafilters and modal logic, see “Sobel on Goedel’s Ontological Proof” by Robert C. Koons

Incomparable degrees of unsolvability

I started talking with Post regularly. He gave me a batch of his reprints. John Stachel and I asked Post if we could do a reading course with him in mathematical logic. That was in my junior year. We didn’t get very far in the course, because Post had one of his breakdowns after a few weeks. He had just made an important discovery regarding incomparable degrees of unsolvability, and the excitement was too much for him and pitched him over into the manic phase. We didn’t see him again for some months.
…
Particularly logicians seem to be prone to it! In fact, I had a joke with John Stachel. Post had lost an arm in a childhood accident. Hans Reichenbach, who was sort of a logician and a philosopher, came to City College for a semester to give some courses, and he was essentially stone deaf. Church had vision problems—he had bad cataracts, which in those days was much more of a problem than it is today. So the joke was that, if I’m going to be a logician, maybe I should give up a finger now, instead of something worse!

(*)

From the AMS Notices interview with Martin Davis.

Pêle-mêle

Sublime
Pêle-mêle
Henri Poincaré
D’élégants théorèmes
Prouva sans façons,

Classa des variétés
Difféomorphiquement
Utilisant la dualité
Et du génie aussi.

Autre
Pêle-mêle
Nicolas Bourbaki
Ressuscita de parmi les morts,
Pour les mathématiques sauver,

Débita d’assommants traités
Hypercinétiquement,
Prouvant qu’il aurait dû
Dans la tombe rester.

(*)

Un exemple d’animosité envers Bourbaki est ce double poème d’un goût contestable écrit (en anglais) par Arnold Seiken.

Coordonnées

Soit une multiplicité vectorielle.
Un corps opère seul, abstrait, commutatif.
Le dual reste loin, solitaire et plaintif,
Cherchant l’isomorphie et la trouvant rebelle.

Soudain, bilinéaire, a jailli l’étincelle
D’où naît l’opérateur deux fois distributif.
Dans les rets du produit tous les vecteurs captifs
Vont célébrer sans fin la structure plus belle.

Mais la base a troublé cet hymne aérien:
Les vecteurs éperdus ont des coordonnées.
Cartan ne sait que faire et n’y comprend plus rien.

Et c’est la fin. Opérateurs, vecteurs, foutus.
Une matrice immonde expire. Le corps nu
Rentre en lui-mêm, au sein des lois qu’il s’est données.

(*)

Sonnet composé par André Weil au congrès de Chançay (septembre 1937).