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Showing 1 to 6 of 6 for “"axiom of choice"”.
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Free groups and the axiom of choice
… Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise in this context, such as whether the same is true for free abelian groups, …
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A Proof That Every Set Can be Well-Ordered.
The purpose of this paper is to show that the Well-Ordering Theorem is a consequence of the Axiom of Choice via the Moore-Zermelo Proposition. The work herein is completely my own and is not the result of suggestions made by any other person.
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Independence and conservativity results for intuitionistic set theory
… uniqueness condition, CT0!, and the general form of Church's thesis, CT0. The objective here is to extend Lifschitz' realizability to intuitionistic Zermelo-Fraenkel set theory with two sorts, IZFN. In addition to separating Church's thesis with uniqueness condition from its general form in …
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A defence of predicativism as a philosophy of mathematics
A specification of a mathematical object is impredicative if it essentially involves quantification over a domain which includes the object being specified (or sets which contain that object, or similar). The basic worry is that we have no non-circular way of understanding such a specification. …
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Předpovídání budoucnosti a axiom výběru
… její budoucí hodnoty z předcházejícího vývoje. Z axiomu výběru ovšem vyplývá existence strategie, která na základě hodnot funkce f na nějakém intervalu (s, t) správně předpoví její hodnoty na intervalu [t, t + ) v každém bodě t reálné osy vyjma spočetné množiny. Tento výsledek Alana Taylora a …
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Some results in set theory
L'abstract è presente nell'allegato / the abstract is in the attachment