ABSTRACT. D ?i) The class of the axiomatic foundations mentioned in the title is called Ax Found; and its structure is treated in the introduction. ?ii) This consists of Parts A to G followed by the References. ?iii) In [17] Bressan's modal logic is treate
Rend.Mat.Acc.Linceis.9,v.16:143-157(2005)
Matematica.ÐOnAxiomaticFoundationsCommontoClassicalPhysicsandSpecialRelativity.Nota(*)diALDOBRESSAN.
ABSTRACT.Ð
(i)TheclassoftheaxiomaticfoundationsmentionedinthetitleiscalledAxFound;anditsstructureistreated
intheintroduction.
(ii)ThisconsistsofPartsAtoGfollowedbytheReferences.
(iii)In[17]Bressan'smodallogicistreatedinaconsciouslynon-rigorousway.Insteadhere,aswellasAx
Found,ithasarigoroustreatment.Suchatreatmenthadbeenappreciatedbythemathematicalphysicist
C.Truesdellin[62].
(iv)In1953Truesdellhadaremarkableintuition,whosecorrectnessappearedonlyin1962,fromBressan's
monograph[3].
(v)AsaforeignmemberoftheLinceiAcademy,Truesdellsupportedsomelogicalfeatures,absentinhis
school,andhegaveM.Pitteria``confidentialcopy''involvingthisfact.
(vi)SincethusthepresentrigoroustreatmentofBressan'smodallogicappearsstronglysupportedby
Truesdell,itwasnaturaltodedicatethepresentworktohismemory.
(vii)Intheintroductiononesaystohaveprovedcertainresults(whoseproofdoesnotappearthere)concerning
rationalmechanicsorBressan'smodallogictreatedrigorously.
KEYWORDS:AxiomaticFoundations;SpecialRelativity;ClassicalPhysics;ContinuousMedia.
RIASSUNTO.ÐSuifondamenticomuniallafisicaclassicaeallarelativitaÁristretta.
(i)LaclassedeifondamentiassiomaticimenzionatineltitoloeÁdettabrevementeAxFound;edeÁtrattata
nell'introduzione.
(ii)QuestaconsistenellePartsA,...,GseguitedalleReferences.
(iii)In[17]lalogicamodalediBressaneÁtrattatainmodoconsciamentenonrigoroso.Invecequiessa,alparidi
AxFound,haunatrattazionerigorosa.UnataletrattazioneerastataapprezzatadalfisicomatematicoTruesdellin[62].
(iv)Nel1953Truesdellebbeunanotevoleintuizione,lacuicorrettezzarisultoÁsolonel1962,dallamonografia
[3]diBressan.
(v)ComeSociostranierodeiLincei,Truesdellsostennedegliaspettilogici,assentinellasuascuola.Inoltre
diedeaM.Pitteriuna``confidentialcopy''involgentetalefatto.
(vi)LapresentetrattazionerigorosadellalogicamodalediBressanapparepercioÁfortementesostenutada
Truesdell.Eraquindinaturalededicareallasuamemoriaillavoroinviato.
(vii)Nell'introduzionesidicediaverottenutocertirisultati(lacuidimostrazionenonappareivi)concernentila
MeccanicarazionaleolalogicamodalediBressantrattatarigorosamente.
CONTENTS
PartA:Ontheclassoftheaxiomaticfoundationsmentionedinthetitle.......................PartB:MainreasonsforchangingsomepartsofSection2in(Br&Mont's D)[17].Astrangebutlucky
situation................................................................
PartC:Reasonsforusing``AxFound''andforwritingthepresentworkinmemoryofProf.C.Truesdell
PartD:SomeresultsreadyforinclusioninAxFound.AveryseriousdifficultyovercomebyA.Zanardo144145145150
(*)Pervenutainformadefinitivaall'Accademiail29settembre2005.