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Jailton C. Ferreira

Publications and source records attributed to Jailton C. Ferreira.

11 recordsLinked to original sources
arXiv2026

On the Goedel's formula

The proof of Goedel's first incompleteness theorem includes the construction of an arithmetic formula G that represents the metamathematical statement: the formula G is not provable. This article examines the formula G (of Goedel). We demonstrated that there is no Goedel's number for the formula G if number of provable well formed formulae with one free variable is finite. If there is a non-finite number of provable propositions in the theory, then Goedel's formula also does not possess the Goedel's number.

math.GM↗
arXiv2008

The Antinomy of the Liar and Provability

This work evidences that a sentence cannot be denominated by P and written as P IS NOT TRUE. It demonstrates that in a system in which Q denominates the sentence Q IS NOT PROVABLE it is not provable that Q is true and not provable.

math.GM↗
arXiv2002

On Goldbach's Conjecture

It is shown that if every odd integer $n > 5$ is the sum of three primes, then every even integer $n > 2$ is the sum of two primes. A conditional proof of Goldbach's conjecture, based on Cramér's conjecture, is presented. Theoretical and experimental results available on Goldbach's conjecture allow that a less restrictive conjecture than Cramér's conjecture be used in the conditional proof. A basic result of the Maier's paper on Cramér's model is criticized.

math.GM↗
arXiv2002

On power sets

This work presents theorems which state (i) Z is a proper subset for any bijection f between A and Z, where Z is contained in P(A), A is a non-finite set and |Z|=|A|, and (ii) being Z a proper subset of P(A) nothing affirms or denies that |P(A)|>|A|. Russell's paradox is examined and it is shown that the set of all the ordinary sets does not exist. A mistake in Cantor's proof on cardinality of power sets is shown.

math.GM↗
arXiv2002

Infinite and natural numbers

The infinite numbers of the set M of finite and infinite natural numbers are defined starting from the sequence 0Φ, where 0 is the first natural number, Φis a succession of symbols S and xS is the successor of the natural number x. The concept of limit of the natural number n, when n tends to infinite, is examined. Definitions and theorems about operations with elements of M, equivalence and equality of natural numbers, distance between elements of M and the order of the elements are presented.

math.GM↗
arXiv2001

On the cardinality of the set of the real numbers

It is shown that any denumerable list L to which Cantor's diagonal method was applied is incomplete. However, this doesn't allow us to affirm that the cardinality of the real numbers of the interval [0, 1] is greater than the cardinality of the finite natural numbers. Paper withdrawn (its essential part is included in the version 3 of math.GM/0108119).

math.GM↗