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pro vyhledávání: '"Cattabriga, Paola"'
Autor:
Cattabriga, Paola
We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted one, that a
Externí odkaz:
http://arxiv.org/abs/2409.05903
Autor:
Cattabriga, Paola
Godel numbering is an arithmetization of sintax which defines provability by coding a primitive recursive predicate, Pf(x,v). A multiplicity of researches and results all around this well-known recursive predicate are today widespread in many areas o
Externí odkaz:
http://arxiv.org/abs/2404.04038
Autor:
Cattabriga, Paola
In this article we discuss the proof in the short unpublished paper appeared in the 3rd volume of Godel's Collected Works entitled "On undecidable sentences" (*1931?), which provides an introduction to Godel's 1931 ideas regarding the incompleteness
Externí odkaz:
http://arxiv.org/abs/2403.19665
Autor:
Cattabriga, Paola
To a close reading of the original Turing article of 1936, we can learn it is based on the claim to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the enumeration of the computable sequen
Externí odkaz:
http://arxiv.org/abs/1308.0497
Autor:
Cattabriga, Paola
The conditions for proper definitions in mathematics are given, in terms of the theory of definition, on the basis of the criterions of eliminability and non-creativity. As a definition, Russell's antinomy is a violation of the criterion of eliminabi
Externí odkaz:
http://arxiv.org/abs/0705.0901
Autor:
Cattabriga, Paola
The predicate complementary to the well-known Godel's provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness and decidab
Externí odkaz:
http://arxiv.org/abs/math/0606713
Autor:
Cattabriga, Paola
In 1891 Cantor presented two proofs with the purpose to establish a general theorem that any set can be replaced by a set of greater power. Cantor's power set theorem can be considered to be an extension of Cantor's 1891 second proof and its argument
Externí odkaz:
http://arxiv.org/abs/math/0312360
Autor:
Cattabriga, Paola
This article demonstrates the invalidity of Theorem VI of Godel's monograph of 1931, showing that propositions (15) and (16), derived from definition (8.1), in its proof, are false in PA. This is achieved in two steps. First, the predicate complement
Externí odkaz:
http://arxiv.org/abs/math/0306038