Related papers: A Non-Constructive Proof of Cantor's Theorem

We consider the convergence theory for dyadic approximation in the middle-third Cantor set, $K$, for approximation functions of the form $\psi_{\tau}(n) = n^{-\tau}$ ($\tau \ge 0$). In particular, we show that for values of $\tau$ beyond a…

The ternary Cantor set $C$, constructed by George Cantor in 1883, is probably the best-known example of a perfect nowhere-dense set in the real line, but as we will see later, it is not the only one. The present article will delve into the…

Cook and Reckhow 1979 pointed out that NP is not closed under complementation iff there is no propositional proof system that admits polynomial size proofs of all tautologies. Theory of proof complexity generators aims at constructing sets…

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove…

A theorem, usually attributed to Barr, yields that (A) geometric implications deduced in classical L_{\infty\omega} logic from geometric theories also have intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its proof…

We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to…

In this paper we prove a conjecture that $D(4)$-quintuple does not exist using both classical and new methods. Also, we give a new version of the Rickert's theorem that can be applied on some $D(4)$-quadruples.

We construct a combinatorially large measure zero subset of the Cantor set.

We give a slightly different proof of the NTV conjecture for the Hilbert transform that was proved by T. Hyt\"onen, M. Lacey, E.T. Sawyer, C.-Y. Shen and I. Uriarte-Tuero, building on previous work of F. Nazarov, S. Treil and A. Volberg.…

We prove that there exists a nonprincipal ultrafilter $\mathcal U$ on $\mathbb N$ such that for every countable (or separable) structure $B$ in a countable language the quotient map from the reduced product associated with the Fr\'echet…

The no-supervenience theorem limits the capacity of physicalist theories to provide a comprehensive account of human consciousness. The proof of the theorem is difficult to formalize because it relies on both alethic and epistemic notions…

Czachor's recent proposal introduces a form of non-Newtonian calculus built by pulling back arithmetic operations through arbitrary bijections between continua. Although the idea is mathematically inventive, it runs into serious conceptual…

Carleson's Theorem asserts the pointwise convergence of Fourier series of square integrable functions. We give a complete proof, following joint work of the author and C. Thiele. Over 20 exercises are also detailed. We also discuss the…

In the early 2000's the first and second named authors worked for a period of six years in an attempt of proving the Compositional Shuffle Conjecture [1]. Their approach was based on the discovery that all the Combinatorial properties…

In this paper we give a counterexample to the conjecture: Let $S\in{\rm SInn}$. Then $z\cdot S$ is onto $U$.

A numeral system is an infinite sequence of different closed normal $\lambda$-terms intended to code the integers in $\lambda$-calculus. H. Barendregt has shown that if we can represent, for a numeral system, the functions : Successor,…

We prove a noncommutative variant of Saskin's classical theorem -- on the connection between Choquet boundaries for function spaces and Korovkin sets -- for operator systems generating separable Type I C*-algebras. The main result implies…

We introduce a notion of density point and prove results analogous to Lebesgue's density theorem for various well-known ideals on Cantor space and Baire space. In fact, we isolate a class of ideals for which our results hold. In contrast to…

We prove some theorems on decomposable continua. In particular, we prove; (i) the property of being a Wilder continuum is not a Whitney reversible property, (ii) inverse limits of D**-continua with surjective monotone upper semi-continuous…