Rend. Mat. Acc. Lincei s. 9, v. 16143-157 2005) Matematica.

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.