Skolem's Paradox and Quantum Information. Relativity of Completeness à la Gödel

1 Васил Пенчев ПАРАДОКСЪТ НА СКУЛЕМ И КВАНТОВАТА ИНФОРМАЦИЯ. ОТНОСИТЕЛНОСТ НА ПЪЛНОТА ПО ГЬОДЕЛ Abstract. In 1992, Thoralf Skolem introduced the term of «relativity» as to infinity or set theory. He demonstrated by Zermelo’s axiomatics of set theory... More

1 Васил Пенчев ПАРАДОКСЪТ НА СКУЛЕМ И КВАНТОВАТА ИНФОРМАЦИЯ. ОТНОСИТЕЛНОСТ НА ПЪЛНОТА ПО ГЬОДЕЛ Abstract. In 1992, Thoralf Skolem introduced the term of «relativity» as to infinity or set theory. He demonstrated by Zermelo’s axiomatics of set theory (incl. the axiom of choice) that there exist unintended interpretations of any infinite set. The very notion of set was also «relative». We can apply his argumentation to Gödel’s incompleteness theorems as well as to his completeness theorem (1930). Then both the incompleteness of Peano arithmetic and the completeness of first-order logic turn out to be also «relative» in Skolem’s sense. Skolem’s «relativity» argumentation of that kind can be applied to a very wide range of problems and can be spoken of the relativity of discreteness and continuity, of finiteness and infinity, of Cantor’s kinds of infinities, etc. The relativity of Skolemian type helps us for generalizing Einstein’s principle of relativity from the invariance of th Less