Related papers: (Seemingly) Impossible Theorems in Constructive Ma…
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
In the paper it is demonstrated that Bells theorem is an unprovable theorem.
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
Recent studies showed that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for…
This essay contains three parts. The first part of essay focuses on the hypothesis of the functional semantic constructions (FSC-Hypothesis). This hypothesis explains that a language, a number, a money are the functional semantic…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…
Recently, Artemov [4] offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.
In this paper, we prove a structure theorem for the infinite union of $n$-adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in 1998, and as a by product, we also prove a classification…
An technically interesting proof of a known theorem.
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expected, as the obstruction arises in odd rather than even…
We investigate the reasons of having confidence in mathematical theorems. The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to this confidence. Opposing…
Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…