Related papers: Todas as afirma\c{c}\~oes verdadeiras s\~ao demons…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
We illustrate the concept of mathematical proof.
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that…
We study the formalized v statement by allowing the occurrence of different arrays of quantifiers in it. We prove that for some specific arrays of quantifiers we get consistency statements that are S-equivalent to the original…
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A$ of a computably enumerable, model complete theory, the…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In…
A very simple but useful almost sure convergence theorem of probability is given.
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
We introduce Probabilistic Regular Expressions (PRE), a probabilistic analogue of regular expressions denoting probabilistic languages in which every word is assigned a probability of being generated. We present and prove the completeness…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…