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ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী
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Меѓународни кривични трибунали.docx
Postgraduate Study Program of Nutrition and Food Science
The Elaborate_ The first Postgraduate Study of Nutrition and Food Science in Macedonia as the first step towards an action-oriented cooperative process between Higher Education-University and Food Industry. Coordinator: Vera Simovska, MD., PhD, subspec. for hygiene of nutrition for healthy and sick people, spec. of sports medicine and public health. (Accrediated by the University and Goverment Commission for higher education)
Science and Industry
Томас Фей. Логика срещу автентично мислене
ISSN 0861-7899 Философски алтернативи Philosophical alternatives СIlliСАНИЕ НА ИНСТИТУТА 3-4/2000
Мартин Хайдегер. Стихотворението
Философски алтернатцви Philosophical alternatives СПИСАНИЕ НА ИНСТИТУТА 1/2000 ЗА ФИЛОСОФСКИ ИЗСЛЕДВАНИЯ ГОДИНА IX VOL. IX
М. Чапек. Логиката на твърдите тела от Платон до Куайн
ISSN 0861 -7899 Философски алт~рнативи Philosophical alternatives 5-6/1999 СПИСАНИЕ НА ИНСТИТУТА
Рафъл Фолк. Какво е ген?
ISSN 0861-7899 ИЛОСОфСКli ' алтер'пативи о а.. ~ :tеI4r1а(iVёg 3-4/1
Black Box testing software
Дончо Борисов Black Box тестирање ПРВ ПРИВАТЕН ЕВРОПСКИ УНИВЕРЗИТЕТ РЕПУБЛИКА МАКЕДОНИЈА СЕМИНАРСКА РАБОТА Black Box тестирање Студент : Дончо Борисов 0002/09 1 Дончо Борисов
Black Box Testing
Gentzen's theorem for the transfinite foundation of Peano arithmetic
Abstract: Gentzen’s completeness theorem of arithmetic by transfinite induction until ε_0 is very important to us. His argumentation was constructivist or even finitist’s one. He claimed that transfinite induction (contrary to its name) is a finitary method. According to us, it is mere the sequential undecidable statement. We would prefer an �actualist� reinterpretation of it: both finiteness and infinity until ε_0 together are dual and complementary. Peano arithmetic (including the principle of complete induction) can found infinity until ε_0 being the metatheory or metalanguage of Gentzen arithmetic comprising both of the finite numbers and infinite ordinals (less than ε_0). In its turn, Gentzen arithmetic (i.e. Peano axiomatics, in which complete induction is generalized to transfinite induction until ε_0) can found Peano arithmetic being the metatheory or metalanguge of it. Peano arithmetic and Gentzen arithmetic have almost the same axiomatics. Each of them can serve as metalanguage as object language of the other. They are correlative each to other in the manner of Skolem. Describing such a case, we may introduce the term of dual (dualistic, mutual) foundation (also �dual-foundation� instead of �self-foundation� as well as �dual-reference� instead of �self-reference�) in relation to the completeness of arithmetic. The common and mutually relative (in Skolemian sense) principle of complete and transfinite induction can be generalized as counting: an unity can always be added to any (1) finite or (2) infinite number (ordinal) as well as (3) between the �last� finite number and the �first� infinite ordinal (the principle of constructivism). Any unity, added wherever, is the same. So, constructivism rather universalizes counting to be the base for introducing infinity, than only to extend it over the domain on infinity. A decisive point is (3). How many unities should be added to a finite number to be gained an infinite one (ordinal): one, some or any finite numb
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