Rend. Mat. Acc. Lincei s. 9, v. 16143-157 2005) Matematica.(11)

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

ONAXIOMATICFOUNDATIONSCOMMONTOCLASSICALPHYSICS...153AS16,1Iftheyear19RSisnotearlierthan2000,theninthecasesy 1andy>1IregardBressanRS=Bressan19RSandBressanaiRS=Bressanai19RS(i 1;...;y)respectively.

AS16,2Theaboverules,wheny 1,include[5]andmoregenerally[1,2]andAS1;7too;andwheny>1theyinclude[9]and[10].

AS16,3Notethat[9]and[10]aretheonlycaseswithlabelswhoseabbreviationsareexplicitlymentionedinourreferences.

AS17TheseriesofworkscalledAxFoundincludesthepresentIntroduction,whichisclassifiedbyx1-seebelowtheprecedingContents.

AS17,1Usuallyaparagraphofagivenpageismeantasacertainsetoflines.

AS17,2Istatethatineverycontributingwork(toAxFound),theboldentryofanyparagraphoftheformxt1-seeAS15-mustbeprintedatthelinewherethisparagraphstarts.Furthermore,(a)followingaUniversityofTorino(Turin),thenotboldASr[ASr;s]can(everywhere)beusedtomentiontheboldASr[ASr;s]-cf.AS15.Hence,inordertomentionaparticularoccurrenceofASr[ASr;s],onehastospecifyitbyusing:``ASr''[``ASr;s''].

AS18TheworksinterestingAxFound,e.g.,contributingworks,formabookbeingconstructed-seeAS1;1-.Furthermore

AS18,1generallytheymainlyhavecertainfeatureshintedatinAS1toAS1;2,andmoreclearlyshowninAS2toAS3,AS4;3,AS7;3(especiallyin(g)),inAS7;5,andlastlyin(theremark)AS7;6dealingwithmylongarticleMet.

AS18,2(a)InAS1onespeaks,e.g.,ofabookbeingconstructed,withdevelopmentsimperfectlyknown.(b)Inthepresentpaperthenotationsx1,x2,etc.,aremeant,Ithink,inamannerwiderthantheusualone,andhencedifferentfromthis.(g)By(a)theanaloguesofthepropertiesconsideredforthesequenceAS1,...;AS1;8inx1holdforeverysimilarsequenceAS1,...,AS1;l,...;writteninanypaperlaterthanx1,(e.g.,calledx2.)(d)Assumenowthatx2hasbeenprinted.Then(d1)anarbitrarymarkASlorASl;m,writteninx1determinesthepagesofx2whereithasbeenprinted.Furthermore(d2)thefollowingadvantagesappear:(1o)thismarkgivesinformationmoreprecisethantheonegivenbythepageswherethemarkisprinted;(2o)itmaybeused,e.g.,inthepaperx2(evenifinx2thismarkisnotused)-cf.thepoint(3)aboveAS5inx1-.(d3)NowfixanarbitrarysPZ>0andconsidertheanalogueforpaperxs,ofwhathasbeensaidaboutx1(thepaperxsbeingsupposedtoexist).(d4)Thus,briefly,asequenceofpapersx(2);x(3);...similartox2canbeconsidered.