Related papers: On The Composition Lemma
We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem.…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
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.
Wrong assumptions were made in the proof of Theorem 3.12 and Lemma 3.6. A preprint containing a correct proof for Lemma 3.6 is in preparation and will be uploaded later this month. So the results of section 3 are correct, apart from Theorem…
We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
We present several results, including some remarks on the Hopf Lemma.
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
This is an elementary explanation of a cubic composition formula due to Ramanujan.
Recently, Ivan Mihajlin and Alexander Smal proved a composition theorem of a universal relation and some function via so called xor composition, that is there exists some function $f:\{0,1\}^n \rightarrow \{0,1\}$ such that…
Determining if two protocols can be securely composed requires analyzing not only their additive properties but also their destructive properties. In this paper we propose a new composition method for constructing protocols based on…
We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.
We present an argument for {\em construction grammars} based on the minimum description length (MDL) principle (a formal version of the Ockham Razor). The argument consists in using linguistic and computational evidence in setting up a…
We prove that for any coloring of the naturals using two colors there are monochromatic sets of the form $\{x,y,xy,x+iy:i\leq k\}$ and $\{x,y,x^y,xy^i:i\leq k\}$ for any $k$.
We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).
We present a framework to formally describe probabilistic system behavior and symbolically reason about it. In particular we aim at reasoning about possible failures and fault tolerance. We regard systems which are composed of different…
We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.