Rend. Mat. Acc. Lincei s. 9, v. 16143-157 2005) Matematica.(2)

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

144A.BRESSANPartE:OnMontanaro'scollaborationtoBr&Mont,substantiallywithinhisdegreethesis;andonhis

subsequentpapers,inpartveryimportantorevensurprising.........................151

PartF:Sometechnicalpreliminaries.Howassertionscanbereferredtoandhowcontentsareusedinthe

Introductionorincontributingworks.Onsymbolsused,e.g.,inspeakinginEnglishaboutworks

writteninItalian.OnAbbreviations............................................151

PARTA:ONTHECLASSOFTHEAXIOMATIC

FOUNDATIONSMENTIONEDINTHETITLE

Thereisauniqueincreasingseriesofinstantst0;t1;t2;...suchthat,forr 0;1;...,attrsomeassertionsbelongingtoaxiomaticfoundationsbegintobeknown.TheseassertionsconstituteaworkwrcalledcontributiontoAxFound.Theworksw0;w1;...arebrieflydenotedby``ContrWs''andforpracticalmotivesseeAS2andAS2;1below.Ofcourse,forr 0;1;2;...,attrthecontributingworkswr 1;wr 2;...,arenotknown.ThestudyofAxFound-see(i)intheAbstract-isstronglybasedonBr&Mont D[7]-see(AS1;3toAS1;7andmainly)AS1;6below-andaimsatimprovingandamplifying[7].AS1Thementionedcontributingworksareconsecutiveinthattheyformauniqueseries(likeiftheywerechaptersorgroupsofchaptersinasamebook.Thisbookisbeingconstructedanditspossibledevelopmentswillgenerallybeatmostimperfectlyknown).

AS1,2Differentcontributionsmightbepublishedondifferentscientificjournals.AS1,3Ishalluse(alsobutnotonly)`Pitteri03'asanabbreviationforPitteri'spaperpublishedontheJournalofElasticity72,241-261,2003.Thisfactalsoappearsfrom[60].

AS1,4Inref.(i.e.reference)[16](onp.261)ofPitteri2003itisshownhowtoobtainanextendedversionofit,whichIshalldenoteby`ExtendPitt'-e.g.,inordertoobtainExtendPittonecanalsosee[61].

AS1,5InsomeentriesoftheReferencesofthepresent§1,someabbreviationsareexplicitlyaddedwithinparentheses:e.g.,suchadditionsareperformedin[3,4]and[5]bymeansof` DMet',` DGIMC',and` DBressan1974'inordertorespectivelyintroducetheabbreviations`Met',`GIMC'and`Bressan1974'.

AS1,6Besidesusing`Br&Mont'for[17],Icanabbreviate[48](onp.27)inExtendPitt,i.e.,(theonly)Truesdell's654pagebook,by`Truesdell1984'.

AS1,7MoredetailsonabbreviationscanbefoundinPartF.

AS1,8Letusexplicitlyremarkthat,e.g.,withinAS2orAS2;3,AShastobereadasassertionorsubassertionrespectively.

FurthermoreImeaneverysuchassertionasanassertionsetoranassertionconjunction;andIregardeverysubassertionASr;sasanassertionheadedbyASr(forinstancebelongingtoASr).