相关论文: Cox's Theorem Revisited
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…
We document some versions, in real K-theory, of well-known properties of the coarse assembly map in complex K-theory. These results are well-known, but difficult to find in the literature.
There are given conditions for represention of a function of many arguments as the difference of convex functions.
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
We briefly discuss the current state, and future computational implications, of quantum type theory.
The realizability of countable Cox configurations on Miquelian planes is proved. A simple way to determine the automorphisms of the Cox configurations is presented.
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
Popper's original thought experiment probed some fundamental and subtle rules of quantum mechanics. Two experiments have directly and indirectly tested Popper's hypothesis, but they seem to give contrasting results. The equations governing…
It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory $T$, the next strongest natural theory is $T+\mathsf{Con}_T$. We formulate and prove a statement…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical set-theoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be…
The actual existence of collections of universes -- multiverses -- is strongly suggested by leading approaches to quantum cosmology, and has been proposed earlier as an attractive way to explain the apparent fine-tuned character of our…
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
A new proof of Oka's lemma is given for smoothly bounded, pseudoconvex domains $D\subset\mathbb{C}^n$. The method of proof is then also applied to other convexity-like hypotheses on the boundary of $D$.
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…