Related papers: Godel's theorem is invalid
The prenex fragments of first-order infinite-valued Goedel logics are classified. It is shown that the prenex Goedel logics characterized by finite and by uncountable subsets of [0, 1] are axiomatizable, and that the prenex fragments of all…
We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of G\"odel. A typical stably computably enumerable set is the set of Diophantine equations with no integer…
In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in…
Glivenko's theorem says that, in propositional logic, classical provability of a formula entails intuitionistic provability of double negation of that formula. We generalise Glivenko's theorem from double negation to an arbitrary nucleus,…
Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…
The problem is posed of establishing a possible relationship between a new type of Multi-verse representation, G\"odel undecidability theorems and the logic of classical, quantum mechanics and quantum gravity. For this purpose example cases…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
The only fault we can fairly lay at Lucas' and Penrose's doors, for continuing to believe in the essential soundness of the Goedelian argument, is their naive faith in, first, non-verifiable assertions in standard expositions of classical…
Recently, we had to realize that more and more game theoretical articles have been published in peer-reviewed journals with severe logical deficiencies. In particular, we observed that the indirect proof was not applied correctly. These…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.
In this paper, we systematically apply Grothendieck duality theorem to simplify the proofs of several theorems in different papers: Including a vanishing theorem in KMM, a theorem of Koll\'{a}r's paper, a vanishing theorem due to Kov\'{a}cs…
It is shown that the Einstein-Podolsky-Rosen conclusion concerning the `incompleteness' of Quantum Mechanics is invalidated by two logical errors in their argument. If it were possible to perform the proposed gedanken experiment it would,…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
The conventional decomposition of a vector field into longitudinal (potential) and transverse (vortex) components (Helmholtz's theorem) is claimed in [1] to be inapplicable to the time-dependent vector fields and, in particular, to the…
We discuss an incompleteness result proven by Bezboruah and Shepherdson. This result tells us that the weak theory ${\sf PA}^-$ does not prove the consistency of any theory (under certain assumptions explained in the paper). Kreisel argued…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
In his ontological argument G\"{o}del says nothing about its underlying logic. The argument is modal and at least of second-order and since S5 axiom is used so it is widely accepted that the logic of the argument is the S5 second-order…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…