110 http://isa.epfl.ch/imoniteur_ISAP/ itffichecours.txt?path=EPFL.Etu.FicheCours.HeaderEN itffichecours.txt?path=EPFL.Etu.FicheCours.GlobalNav_js en 2026 944590 6683117 944590 2305107546 2305107546 0 0 Mathematics MA SB Faculté des sciences de base School of Basic Sciences !itffichecours.htm?ww_i_matiere=230597543&ww_x_anneeAcad=2305107546&ww_i_section=944590&ww_i_niveau=6683117 1696552884 1696552963 2024-2025 LIVRET DE COURS MATH-381 Logique mathématique Mathematical logic Enseignants Duparc Jacques Langue d'enseignement français Cursus Mathématiques(2024-2025, MA - Bachelor 2022)
SemestreOblig.OptionFilières
BA5x
 Crédits 5 Session Hiver Charge 150h Examen Ecrit Nombre de places Semestre Automne Semaines 14 Heures 4 hebdo
Cours 2 hebdo
Exercices 2 hebdo
Plan d'étude SemestreOblig.OptionFilières
Mathématiques 2024-25BA5x
Cursus Sem. Type
Mathématiques BA5 Opt.
Résumé Branche des mathématiques en lien avec le fondement des mathématiques et l'informatique théorique. Le cours est centré sur la logique du 1er ordre et l'articulation entre syntaxe et sémantique. Contenu

Eléments de théorie naïve des ensembles. Bons ordres, nombres ordinaux et cardinaux. Axiome du Choix, Lemme de Zorn et Théorème de Zermelo.


Logique du 1er ordre :


- Syntaxe : langage, formule et arbres de décomposition, variable libre vs liée, formule close, substitution.


- Sémantique : structure et réalisation, sous-structure et restriction. Homomorphisme et isomorphisme. Interprétation et satisfaction. Jeux d'évaluation. Equivalence universelle et conséquence sémantique. Théorie, modèle et consistance. Système complet de connecteur, formes normales prénexes et forme de Skolem. Eléments de théorie des modèles. Ultrapuissance et ultraprodruits. Théorème de compacité et modèles non standard.


- Théorie de la démonstration : systèmes de Hilbert, déduction naturelle et calcul des séquents. Logique classique vs logique intuitionniste vs logique minimale. Elimination des coupures et propriété de la sous-formule. Théorème de complétude de la logique classique (Gödel). Modèles de Kripke et théorème de complétude de la logique intuitionniste.

 

 Mots-clés

Logique mathématique, logique du 1er ordre, syntaxe, sémantique, modèle,  démonstration, fondement des mathématiques, conséquence, consistance, contradiction, théorie, formule, conncecteur, terme, langage, complétude.

 Acquis de formation A la fin de ce cours l'étudiant doit être capable de:
  • Evaluer une formule dans un modèle
  • Formuler une hypothèse
  • Interpréter une théorie
  • Prouver de manière syntaxique
  • Théoriser un concept mathématique
  • Justifier les conséquences sémantique
  • Construire des modèles
  • Concevoir des démonstrations
 Méthode d'enseignement

Cours ex cathedra et exercices

 Travail attendu
  • Participation aux cours
  • Résolution des exercices
 Méthode d'évaluation

Ecrit : 3 heures. Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

 Encadrement Office hours Oui Assistants Oui Forum électronique Oui Ressources Service de cours virtuels (VDI) Non Bibliographie
  • Polycopié distribué en cours

 

  • Introduction générale à la logique mathématique :
  1. René Cori, Daniel Lascar: Introduction à la logique mathématique, vol. 1 et 2, Dunod, 2003
  2. Karim Nour, René David, Christophe Raffalli, et Pierre-Louis Curien: Introduction à la logique : Théorie de la démonstration, Dunod, 2004
  3. H.-D. Ebbinghaus, J. Flum, and W. Thomas: Mathematical Logic, Springer, 1996
  4. Wolfgang Rautenberg: A concise introduction to mathematical logic, Springer, 2006
  5. Yu. I. Manin: A course in mathematical logic, Springer, 1977
  6. Joseph R. Shoenfield: Mathematical Logic, AK Peters, 2001
  7. Elliott Mendelson: Introduction to mathematical logic (4th edition), Chapman & Hall/CRC 1997
  8. George Boolos, John Burgess, Richard Jeffrey: Computability and Logic (5th edition), Cambridge 2007
  9. Herbert B. Enderton : A mathematical introduction to logic (2nd edittion), 2000
  10. Jon Barwise: Handbook of mathematical logic, North-Holland, 1982
  • Théorie des ensembles :
  1. Thomas Jech: Set theory, Springer 2006
  2. Kenneth Kunen: Set theory, Spirnger, 1983
  3. Jean-Louis Krivine: Theory des ensembles, 2007
  4. Patrick Dehornoy: Logique et théorie des ensembles; Notes de cours, FIMFA ENS: http://www.math.unicaen.fr/~dehornoy/surveys.html
  5. Yiannis Moschovakis: Notes on set theory, Springer 2006
  6. Karel Hrbacek and Thomas Jech: Introduction to Set theory, (3d edition), 1999
  • Théorie des modèles :
  1. Bruno Poizat: Cours de Théorie des Modèles. Nur alMantiq walMa'arifah, Villeurbanne, 1985
  2. Wilfrid Hodges: A shorter model theory, Cambridge 1999
  3. Wilfrid Hodges: Model theory, Cambridge, 2008
  4. David Marker : Model theory, an introduction, 2002
  5. Philipp Rothmaler: Introduction to model theory, 2000
  • Théorie de la récursion :
  1. Piergiorgio Odifreddi: Classical recursion theory, vol. 1 and 2, Springer, 1999
  2. Robert I. Soare: Recursively Enumerable Sets and Degres, A Study of Computable Functions and Computably Generated Sets, Springer-Verlag 1987
  3. Nigel Cutland: Computability, an introduction to recursive function theory, 1980
  4. Raymond M. Smullyan: recursion theory for methamathematics, Oxford, 1993
  • Théorie de la démonstration :
  1. Wolfram Pohlers: Proof Theory, the first step into impredicativity, Springer, 2008
  2. A. S. Troelstra, H. Schwichtenberg, and Anne S. Troelstra: Basic proof theory, Cambridge, 2000
  3. S.R. Buss: Handbook of proof theory, Springer, 1998
  • Résultats de Gödel :
  1. Raymond M. Smullyan: Gödel's incompleteness theorems, Oxford, 1992
  2. Peter Smith: An introduction to Gödel's theorems, Cambridge,  2008
  3. Torkel Franzen: Inexhaustibility, a non exhaustive treatment, AK Peteres, 2002
  4. Melvin Fitting: Incompleteness in the land of sets, King's College, 2007
  5. Torkel Franzen: Gödel's theorem: an incomplete guide to its use and abuse, AK Peters, 2005
 Ressources en bibliothèque
  • A course in mathematical logic / Manin http://library.epfl.ch/beast?isbn=0387902430
  • Gödel's incompleteness theorems / Smullyanhttp://library.epfl.ch/beast?isbn=0195046722
  • Model theory / Hodgeshttp://library.epfl.ch/beast?isbn=9780521304429
  • Introduction to model theory / Rothmaler http://library.epfl.ch/beast?isbn=9056992872
  • An introduction to Gödel's theorems / Smith http://library.epfl.ch/beast?isbn=9780521857840
  • Incompleteness in the land of sets / Fittinghttp://library.epfl.ch/beast?isbn=9781904987345
  • Computability and Logic / Booloshttp://library.epfl.ch/beast?isbn=0521234794
  • Handbook of mathematical logic / Barwisehttp://library.epfl.ch/beast?isbn=9780444863881
  • Computability / Cutland http://library.epfl.ch/beast?isbn=0521223849
  • Recursively Enumerable Sets and Degres / Soarehttp://library.epfl.ch/beast?isbn=3540152997
  • Basic proof theory / Troelstrahttp://library.epfl.ch/beast?isbn=0521779111
  • Gödel's theorem / Franzenhttp://library.epfl.ch/beast?isbn=9781568812380
  • Logique et théorie des ensembles / Dehorny http://www.math.unicaen.fr/~dehornoy/surveys.html
  • Classical recursion theory 2 / Odifreddihttp://library.epfl.ch/beast?isbn=044450205X
  • Model theory / Marker http://library.epfl.ch/beast?isbn=0387987606
  • Inexhaustibility, a non exhaustive treatment / Franzenhttp://library.epfl.ch/beast?isbn=1568811748
  • Proof Theory, the first step into impredicativity / Pohlershttp://library.epfl.ch/beast?isbn=9783540693185
  • Introduction to Set theory / Hrbacekhttp://library.epfl.ch/beast?isbn=0824765702
  • Handbook of proof theory / Busshttp://library.epfl.ch/beast?isbn=0444898409
  • Set theory / Jechhttp://library.epfl.ch/beast?isbn=3540440852
  • Notes on set theory / Moschovakis http://library.epfl.ch/beast?isbn=9780387287225
  • Classical recursion theory 1 / Odifreddihttp://library.epfl.ch/beast?isbn=0444872957
  • Introduction to mathematical logic / Mendelson http://library.epfl.ch/beast?isbn=9781584888765
  • Théorie des ensembles / Krivine http://library.epfl.ch/beast?isbn=9782842250966
  • recursion theory for methamathematics / Smullyanhttp://library.epfl.ch/beast?isbn=019508232X
  • Introduction à la logique / Nour http://library.epfl.ch/beast?isbn=2100067966
  • Introduction à la logique mathématique / Corihttp://library.epfl.ch/beast?isbn=2225840806
  • Cours de Théorie des Modèles / Poizat http://library.epfl.ch/beast?isbn=9781461264460
  • Mathematical Logic / Ebbinghaushttp://library.epfl.ch/beast?isbn=0387942580
  • A concise introduction to mathematical logic / Rautenberghttp://library.epfl.ch/beast?isbn=9781441912206
  • Mathematical Logic / Shoenfieldhttp://library.epfl.ch/beast?isbn=1568811357
  • A shorter model theory / Hodges http://library.epfl.ch/beast?isbn=0521587131
  • A mathematical introduction to logic / Enderton http://library.epfl.ch/beast?isbn=0122384520
  • Set theory / Kunen http://library.epfl.ch/beast?isbn=0444854010
Polycopiés

Distribué pendant le cours.

 Liens Moodle Préparation pour
  • MATH-318 Set Theory
  • MATH-483 Gödel and Recursivity
 Mathématiques, 2024-2025, Bachelor semestre 5 Mathematics, 2024-2025, Bachelor semester 5 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Bachelor semestre 5 BA5 HIVER Bachelor semester 5 BA5 Mathématiques MA Mathematics MA
Mathématiques MA Mathematics MA
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Duparc Jacques 183376
Mathématiques MA Mathematics MA
2 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Duparc Jacques 183376
Mathématiques MA Mathematics MA
230597543 Logique mathématique Mathematical logic 5
Ecrit Written Crédit Credits 5 Session hiver Session winter HIV HIV
BALISES_TEXTES BOOLEAN_Symbol BaliseJS_debut BaliseJS_fin Balise_debut Balise_fin FO_debut FO_fin HTML_debut HTML_fin JS_debut JS_fin BALISE_BOLD BOOLEAN_Symbol BaliseJS_debut \x5bb\x5d BaliseJS_fin \x5b\x2fb\x5d Balise_debut [b] Balise_fin [/b] FO_debut font-weight=bold FO_fin font-weight=normal HTML_debut <b> HTML_fin </b> JS_debut \x3cb\x3e JS_fin \x3c\x2fb\x3e BALISE_ITALIC BOOLEAN_Symbol BaliseJS_debut \x5bi\x5d BaliseJS_fin \x5b\x2fi\x5d Balise_debut [i] Balise_fin [/i] FO_debut font-style=italic FO_fin font-style=normal HTML_debut <i> HTML_fin </i> JS_debut \x3ci\x3e JS_fin \x3c\x2fi\x3e BALISE_RED BOOLEAN_Symbol BaliseJS_debut \x5bred\x5d BaliseJS_fin \x5b\x2fred\x5d Balise_debut [red] Balise_fin [/red] FO_debut color=#990033 FO_fin color=black HTML_debut <span style="color:#990033;"> HTML_fin </span> JS_debut \x3cspan style="color:#990033;"\x3e JS_fin \x3c\x2fspan\x3e BALISE_TAB BOOLEAN_Symbol BaliseJS_debut \x5btab\x5d BaliseJS_fin Balise_debut [tab] Balise_fin FO_debut [inline]=&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; FO_fin HTML_debut <img src="/images/gestacplus/base/pixel.gif" width="40" height="1"/> HTML_fin JS_debut \x3cimg src="\x2fimages\x2fgestacplus\x2fbase\x2fpixel.gif" width="40" height="1"\x2f\x3e JS_fin BALISE_LIST BOOLEAN_Symbol BaliseJS_debut \x5bli\x5d BaliseJS_fin Balise_debut [li] Balise_fin FO_debut [inline]=&#x2022;&#160;&#160; FO_fin HTML_debut &#x2022;&#160;&#160; HTML_fin JS_debut \x26#x2022;\x26#160;\x26#160; JS_fin CODE5045487 BOOLEAN_Symbol BaliseJS_debut \x5b\x5d BaliseJS_fin Balise_debut [] Balise_fin FO_debut [inline]=&#160; FO_fin HTML_debut &#160; HTML_fin JS_debut \x26#160; JS_fin BALISE_GREEN BOOLEAN_Symbol BaliseJS_debut \x5bgreen\x5d BaliseJS_fin \x5b\x2fgreen\x5d Balise_debut [green] Balise_fin [/green] FO_debut color=#008000 FO_fin color=black HTML_debut <span style="color:#008000;"> HTML_fin </span> JS_debut \x3cspan style="color:#008000;"\x3e JS_fin \x3c\x2fspan\x3e CODE7508550 BOOLEAN_Symbol BaliseJS_debut \x5bblue\x5d BaliseJS_fin \x5b\x2fblue\x5d Balise_debut [blue] Balise_fin [/blue] FO_debut color=#0080FF FO_fin color=black HTML_debut <span style="color:#0080FF;"> HTML_fin </span> JS_debut \x3cspan style="color:#0080FF;"\x3e JS_fin \x3c\x2fspan\x3e BALISE_COURIER BOOLEAN_Symbol BaliseJS_debut \x5bcourier\x5d BaliseJS_fin \x5b\x2fcourier\x5d Balise_debut [courier] Balise_fin [/courier] FO_debut font-family=Courier FO_fin font-family= HTML_debut <font style="font-family:Courier;"> HTML_fin </font> JS_debut \x3cfont style="font-family:Courier;"\x3e JS_fin \x3c\x2ffont\x3e BALISE_SIZE20 BOOLEAN_Symbol BaliseJS_debut \x5b20\x5d BaliseJS_fin \x5b\x2f20\x5d Balise_debut [20] Balise_fin [/20] FO_debut font-size=20pt FO_fin font-size= HTML_debut <font style="font-size:20pt;"> HTML_fin </font> JS_debut \x3cfont style="font-size:20pt;"\x3e JS_fin \x3c\x2ffont\x3e BALISE_SIZE16 BOOLEAN_Symbol BaliseJS_debut \x5b16\x5d BaliseJS_fin \x5b\x2f16\x5d Balise_debut [16] Balise_fin [/16] FO_debut font-size=16pt FO_fin font-size= HTML_debut <font style="font-size:16pt;"> HTML_fin </font> JS_debut \x3cfont style="font-size:16pt;"\x3e JS_fin \x3c\x2ffont\x3e BALISE_SIZE12 BOOLEAN_Symbol BaliseJS_debut \x5b12\x5d BaliseJS_fin \x5b\x2f12\x5d Balise_debut [12] Balise_fin [/12] FO_debut font-size=12pt FO_fin font-size= HTML_debut <font style="font-size:12pt;"> HTML_fin </font> JS_debut \x3cfont style="font-size:12pt;"\x3e JS_fin \x3c\x2ffont\x3e BALISE_SIZE8 BOOLEAN_Symbol BaliseJS_debut \x5b8\x5d BaliseJS_fin \x5b\x2f8\x5d Balise_debut [8] Balise_fin [/8] FO_debut font-size=8pt FO_fin font-size= HTML_debut <font style="font-size:8pt;"> HTML_fin </font> JS_debut \x3cfont style="font-size:8pt;"\x3e JS_fin \x3c\x2ffont\x3e BALISE_BLACKBACK BOOLEAN_Symbol BaliseJS_debut \x5bblackback\x5d BaliseJS_fin \x5b\x2fblackback\x5d Balise_debut [blackback] Balise_fin [/blackback] FO_debut background-color=black FO_fin background-color=white HTML_debut <span style="background-color:black;"> HTML_fin </span> JS_debut \x3cspan style="background-color:black;"\x3e JS_fin \x3c\x2fspan\x3e BALISE_WHITE BOOLEAN_Symbol BaliseJS_debut \x5bwhite\x5d BaliseJS_fin \x5b\x2fwhite\x5d Balise_debut [white] Balise_fin [/white] FO_debut color=white FO_fin color=black HTML_debut <span style="color:white;"> HTML_fin </span> JS_debut \x3cspan style="color:white;"\x3e JS_fin \x3c\x2fspan\x3e CODE47534071 BOOLEAN_Symbol 1 BaliseJS_debut \x5bbeta\x5d BaliseJS_fin Balise_debut [beta] Balise_fin FO_debut [inline]=&#946; FO_fin HTML_debut &#946; HTML_fin JS_debut \x26#946; JS_fin CODE47534435 BOOLEAN_Symbol 1 BaliseJS_debut \x5balpha\x5d BaliseJS_fin Balise_debut [alpha] Balise_fin FO_debut [inline]=&#945; FO_fin HTML_debut &#945; HTML_fin JS_debut \x26#945; JS_fin CODE47551722 BOOLEAN_Symbol BaliseJS_debut \x5bsub\x5d BaliseJS_fin \x5b\x2fsub\x5d Balise_debut [sub] Balise_fin [/sub] FO_debut vertical-align=sub FO_fin vertical-align=baseline HTML_debut <sub> HTML_fin </sub> JS_debut \x3csub\x3e JS_fin \x3c\x2fsub\x3e CODE48535424 BOOLEAN_Symbol 1 BaliseJS_debut \x5bLAMBDA\x5d BaliseJS_fin Balise_debut [LAMBDA] Balise_fin FO_debut [inline]=&#923; FO_fin HTML_debut &#923; HTML_fin JS_debut \x26#923; JS_fin CODE48535666 BOOLEAN_Symbol 1 BaliseJS_debut \x5blambda\x5d BaliseJS_fin Balise_debut [lambda] Balise_fin FO_debut [inline]=&#955; FO_fin HTML_debut &#955; HTML_fin JS_debut \x26#955; JS_fin CODE47551793 BOOLEAN_Symbol BaliseJS_debut \x5bsup\x5d BaliseJS_fin \x5b\x2fsup\x5d Balise_debut [sup] Balise_fin [/sup] FO_debut vertical-align=super FO_fin vertical-align=baseline HTML_debut <sup> HTML_fin </sup> JS_debut \x3csup\x3e JS_fin \x3c\x2fsup\x3e CODE56031535 BOOLEAN_Symbol 1 BaliseJS_debut \x5bdelta\x5d BaliseJS_fin Balise_debut [delta] Balise_fin FO_debut [inline]=&#948; FO_fin HTML_debut &#948; HTML_fin JS_debut \x26#948; JS_fin CODE56073309 BOOLEAN_Symbol 1 BaliseJS_debut \x5bpi\x5d BaliseJS_fin Balise_debut [pi] Balise_fin FO_debut [inline]=&#960; FO_fin HTML_debut &#960; HTML_fin JS_debut \x26#960; JS_fin CODE56074095 BOOLEAN_Symbol 1 BaliseJS_debut \x5bDELTA\x5d BaliseJS_fin Balise_debut [DELTA] Balise_fin FO_debut [inline]=&#916; FO_fin HTML_debut &#916; HTML_fin JS_debut \x26#916; JS_fin CODE56074172 BOOLEAN_Symbol 1 BaliseJS_debut \x5bMU\x5d BaliseJS_fin Balise_debut [MU] Balise_fin FO_debut [inline]=&#924; FO_fin HTML_debut &#924; HTML_fin JS_debut \x26#924; JS_fin CODE56074264 BOOLEAN_Symbol 1 BaliseJS_debut \x5bPI\x5d BaliseJS_fin Balise_debut [PI] Balise_fin FO_debut [inline]=&#928; FO_fin HTML_debut &#928; HTML_fin JS_debut \x26#928; JS_fin CODE56074328 BOOLEAN_Symbol 1 BaliseJS_debut \x5bSIGMA\x5d BaliseJS_fin Balise_debut [SIGMA] Balise_fin FO_debut [inline]=&#931; FO_fin HTML_debut &#931; HTML_fin JS_debut \x26#931; JS_fin CODE56075056 BOOLEAN_Symbol 1 BaliseJS_debut \x5bALPHA\x5d BaliseJS_fin Balise_debut [ALPHA] Balise_fin FO_debut [inline]=&#913; FO_fin HTML_debut &#913; HTML_fin JS_debut \x26#913; JS_fin CODE56075186 BOOLEAN_Symbol 1 BaliseJS_debut \x5bBETA\x5d BaliseJS_fin Balise_debut [BETA] Balise_fin FO_debut [inline]=&#914; FO_fin HTML_debut &#914; HTML_fin JS_debut \x26#914; JS_fin BALISE_SYMBOL BOOLEAN_Symbol BaliseJS_debut \x5bsymbol\x5d BaliseJS_fin \x5b\x2fsymbol\x5d Balise_debut [symbol] Balise_fin [/symbol] FO_debut font-family=Symbol FO_fin font-family= HTML_debut <font style="font-family:Symbol;"> HTML_fin </font> JS_debut \x3cfont style="font-family:Symbol;"\x3e JS_fin \x3c\x2ffont\x3e CODE56072935 BOOLEAN_Symbol 1 BaliseJS_debut \x5bmu\x5d BaliseJS_fin Balise_debut [mu] Balise_fin FO_debut [inline]=&#956; FO_fin HTML_debut &#956; HTML_fin JS_debut \x26#956; JS_fin CODE56073842 BOOLEAN_Symbol 1 BaliseJS_debut \x5bsigma\x5d BaliseJS_fin Balise_debut [sigma] Balise_fin FO_debut [inline]=&#963; FO_fin HTML_debut &#963; HTML_fin JS_debut \x26#963; JS_fin CODE68199232 BOOLEAN_Symbol 1 BaliseJS_debut \x5bphi\x5d BaliseJS_fin Balise_debut [phi] Balise_fin FO_debut [inline]=&#966; FO_fin HTML_debut &#966; HTML_fin JS_debut \x26#966; JS_fin CODE68199285 BOOLEAN_Symbol 1 BaliseJS_debut \x5bPHI\x5d BaliseJS_fin Balise_debut [PHI] Balise_fin FO_debut [inline]=&#934; FO_fin HTML_debut &#934; HTML_fin JS_debut \x26#934; JS_fin CODE68199991 BOOLEAN_Symbol 1 BaliseJS_debut \x5bgamma\x5d BaliseJS_fin Balise_debut [gamma] Balise_fin FO_debut [inline]=&#947; FO_fin HTML_debut &#947; HTML_fin JS_debut \x26#947; JS_fin CODE68200031 BOOLEAN_Symbol 1 BaliseJS_debut \x5bGAMMA\x5d BaliseJS_fin Balise_debut [GAMMA] Balise_fin FO_debut [inline]=&#915; FO_fin HTML_debut &#915; HTML_fin JS_debut \x26#915; JS_fin CODE68200077 BOOLEAN_Symbol 1 BaliseJS_debut \x5bomega\x5d BaliseJS_fin Balise_debut [omega] Balise_fin FO_debut [inline]=&#969; FO_fin HTML_debut &#969; HTML_fin JS_debut \x26#969; JS_fin CODE68200150 BOOLEAN_Symbol 1 BaliseJS_debut \x5bOMEGA\x5d BaliseJS_fin Balise_debut [OMEGA] Balise_fin FO_debut [inline]=&#937; FO_fin HTML_debut &#937; HTML_fin JS_debut \x26#937; JS_fin CODE72092691 BOOLEAN_Symbol BaliseJS_debut \x5beta\x5d BaliseJS_fin Balise_debut [eta] Balise_fin FO_debut [inline]=&#951; FO_fin HTML_debut &#951; HTML_fin JS_debut \x26#951; JS_fin CODE72092805 BOOLEAN_Symbol BaliseJS_debut \x5bETA\x5d BaliseJS_fin Balise_debut [ETA] Balise_fin FO_debut [inline]=&#919; FO_fin HTML_debut &#919; HTML_fin JS_debut \x26#919; JS_fin BALISE_SOULIGNER BOOLEAN_Symbol BaliseJS_debut \x5bu\x5d BaliseJS_fin \x5b\x2fu\x5d Balise_debut [u] Balise_fin [/u] FO_debut text-decoration=underline FO_fin text-decoration=none HTML_debut <u> HTML_fin </u> JS_debut \x3cu\x3e JS_fin \x3c\x2fu\x3e CODE72092388 BOOLEAN_Symbol BaliseJS_debut \x5bpsi\x5d BaliseJS_fin Balise_debut [psi] Balise_fin FO_debut [inline]=&#968; FO_fin HTML_debut &#968; HTML_fin JS_debut \x26#968; JS_fin CODE72092541 BOOLEAN_Symbol BaliseJS_debut \x5bPSI\x5d BaliseJS_fin Balise_debut [PSI] Balise_fin FO_debut [inline]=&#936; FO_fin HTML_debut &#936; HTML_fin JS_debut \x26#936; JS_fin CODE140502511 BOOLEAN_Symbol 1 BaliseJS_debut \x5brho\x5d BaliseJS_fin Balise_debut [rho] Balise_fin FO_debut [inline]=&#961; FO_fin HTML_debut &#961; HTML_fin JS_debut \x26#961; JS_fin CODE140504636 BOOLEAN_Symbol 1 BaliseJS_debut \x5bRHO\x5d BaliseJS_fin Balise_debut [RHO] Balise_fin FO_debut [inline]=&#929; FO_fin HTML_debut &#929; HTML_fin JS_debut \x26#929; JS_fin CODE148292791 BOOLEAN_Symbol BaliseJS_debut \x5bepsilon\x5d BaliseJS_fin Balise_debut [epsilon] Balise_fin FO_debut [inline]=&#949; FO_fin HTML_debut &#949; HTML_fin JS_debut \x26#949; JS_fin CODE169976220 BOOLEAN_Symbol BaliseJS_debut \x5blig\x5d BaliseJS_fin Balise_debut [lig] Balise_fin FO_debut [inline]=&#x203A;&#160;&#160; FO_fin HTML_debut &#x203A;&#160;&#160; HTML_fin JS_debut \x26#x203A;\x26#160;\x26#160; JS_fin CODE148292899 BOOLEAN_Symbol BaliseJS_debut \x5bEPSILON\x5d BaliseJS_fin Balise_debut [EPSILON] Balise_fin FO_debut [inline]=&#917; FO_fin HTML_debut &#917; HTML_fin JS_debut \x26#917; JS_fin BALISETXT_SAUT BOOLEAN_Symbol BaliseJS_debut \x5bbr\x2f\x5d BaliseJS_fin Balise_debut [br/] Balise_fin FO_debut FO_fin HTML_debut <br/> HTML_fin JS_debut \x3cbr\x2f\x3e JS_fin 230597543 Logique mathématique Mathematical logic French Duparc Jacques 183376 944590