Related papers: An elementary proof that P =/= NP

We present a nonstandard simple elementary proof of Szemer\'{e}di's theorem by a straightforward induction with the help of three levels of infinities and four different elementary embeddings in a nonstandard universe.

We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary…

The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…

We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a hereditary class of relational structures is NIP (resp.…

The paper contains a proof for the P != NP hypothesis with the help of the two "natural" postulates. The postulates restrict capacity of the Turing machines and state that each independent and necessary condition of the problem should be…

We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to \kappa-prime models, for \kappa a regular uncountable cardinal or…

A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer can be represented as the sum of $h$ integers (not necessarily distinct) of $A$. An asymptotic basis $A$ of order $h$ is minimal if no…

Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…

We model physical signals using elements of the algebra of split octonions over the field of real numbers. Elementary particles are corresponded to the special elements of the algebra that nullify octonionic norms (zero divisors). It is…

We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory V$^0_2$ is consistent with the conjecture that NEXP…

In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is…

Using standard techniques from combinatorics, model theory, and algebraic geometry, we prove generalized versions of several basic results in the theory of spectrally arbitrary matrix patterns. Also, we point out a counterexample to a…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

Motivated by the theory of proof complexity generators we consider the following $\Sigma^p_2$ search problem $\mbox{DD}_P$ determined by a propositional proof system $P$: given a $P$-proof $\pi$ of a disjunction $\bigvee_i {\alpha}_i$, no…

We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.

This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference…

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…

We prove two results about generically stable types $p$ in arbitrary theories. The first, on existence of strong germs, generalizes results from D. Haskell, E. Hrushovski and D. Macpherson on stably dominated types. The second is an…

This article concerns the $p$-basic set existence problem in the representation theory of finite groups. We show that, for any odd prime $p$, the alternating group $\A_n$ has a $p$-basic set. More precisely, we prove that the symmetric…