О моделях арифметики в $A$-изолиях.

В.Л. Михеев

Displaying similar documents to “О моделях арифметики в $A$ -изолиях.”

Product sets cannot contain long arithmetic progressions

Dmitrii Zhelezov (2014)

Acta Arithmetica

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Let B be a set of complex numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B = bb’ | b,b’ ∈ B cannot be greater than O((nlog²n)/(loglogn)) and present an example of a product set containing an arithmetic progression of length Ω(nlogn). For sets of complex numbers we obtain the upper bound $O (n^{3 / 2})$ .

Herbrand consistency and bounded arithmetic

Zofia Adamowicz (2002)

Fundamenta Mathematicae

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We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove $T ₘ ⊬ H C o n s^{I ₘ} (T ₘ)$ , where $H C o n s^{I ₘ}$ is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.

Последний вопрос о рекурсивно-перечислимых $m$ -степенях

А. Нис, A. Nis, A. Nis, A. Nis (1994)

Algebra i Logika

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A note on Δ₁ induction and Σ₁ collection

Neil Thapen (2005)

Fundamenta Mathematicae

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Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: " $x^{y}$ exists for some y sufficiently large that x is smaller than some primitive recursive function of y".

On integers of the form $p + 2^{k}$

Laurent Habsieger, Xavier-François Roblot (2006)

Acta Arithmetica

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Automorphisms of models of bounded arithmetic

Ali Enayat (2006)

Fundamenta Mathematicae

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We establish the following model-theoretic characterization of the fragment IΔ₀ + Exp + BΣ₁ of Peano arithmetic in terms of fixed points of automorphisms of models of bounded arithmetic (the fragment IΔ₀ of Peano arithmetic with induction limited to Δ₀-formulae). Theorem A. The following two conditions are equivalent for a countable model of the language of arithmetic: (a) satisfies IΔ₀ + BΣ₁ + Exp; (b) $= I_{f i x} (j)$ for some nontrivial automorphism j of an end extension of that satisfies IΔ₀. Here...

On the weak pigeonhole principle

Jan Krajíček (2001)

Fundamenta Mathematicae

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We investigate the proof complexity, in (extensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of the Ramsey theorem. In particular, we link the proof complexities of these two principles. Further we give lower bounds to the width of resolution proofs and to the size of (extensions of) tree-like resolution proofs of the Ramsey theorem. We establish a connection between provability of WPHP in fragments of bounded arithmetic and cryptographic assumptions...

Aposyndesis in $ℕ$

José del Carmen Alberto-Domínguez, Gerardo Acosta, Maira Madriz-Mendoza (2023)

Commentationes Mathematicae Universitatis Carolinae

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We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions $P (a, b)$ with the property that every prime number that divides $a$ also divides $b$ , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are...

Riesz sequences and arithmetic progressions

Itay Londner, Alexander Olevskiĭ (2014)

Studia Mathematica

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Given a set of positive measure on the circle and a set Λ of integers, one can ask whether $E (Λ) : = e_{λ \in Λ}^{i λ t}$ is a Riesz sequence in L²(). We consider this question in connection with some arithmetic properties of the set Λ. Improving a result of Bownik and Speegle (2006), we construct a set such that E(Λ) is never a Riesz sequence if Λ contains an arithmetic progression of length N and step $ℓ = O (N^{1 - ε})$ with N arbitrarily large. On the other hand, we prove that every set admits a Riesz sequence E(Λ) such that...

Some properties of the class of arithmetic functions $T_{r} (N)$

R. P. Pakshirajan (1963)

Annales Polonici Mathematici

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Fonction de Seshadri arithmétique en géométrie d’Arakelov

Huayi Chen (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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To any adelic invertible sheaf on a projective arithmetic variety and any regular algebraic point of the arithmetic variety, we associate a function defined on $ℝ$ which measures the separation of jets on this algebraic point by the “small” sections of the adelic invertible sheaf. This function will be used to study the arithmetic local positivity.

An inconsistency equation involving means

Roman Ger, Tomasz Kochanek (2009)

Colloquium Mathematicae

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We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations $f (M (x, y)) = A_{φ} (f (x), f (y))$ and $f (A_{φ} (x, y)) = M (f (x), f (y))$ are the constant ones.

A functional equation involving f and $f^{- 1}$ .

J. S. Ratti, Y. -F. Lin (1990)

Colloquium Mathematicae

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Lambert series and Liouville's identities

A. Alaca, Ş. Alaca, E. McAfee, K. S. Williams

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The relationship between Liouville’s arithmetic identities and products of Lambert series is investigated. For example it is shown that Liouville’s arithmetic formula for the sum $\sum_{\binom{(a, b, x, y) \in ℕ ⁴}{a x + b y = n}} (F (a - b) - F (a + b))$ , where n ∈ ℕ and F: ℤ → ℂ is an even function, is equivalent to the Lambert series for $(\sum_{n = 1}^{\infty} (q ⁿ / (1 - q ⁿ)) s i n n θ) ²$ (θ ∈ ℝ, |q| < 1) given by Ramanujan.

On arithmetic progressions on Edwards curves

Enrique González-Jiménez (2015)

Acta Arithmetica

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Let $m \in ℤ_{> 0}$ and a,q ∈ ℚ. Denote by $_{m} (a, q)$ the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve $E_{d} : x ² + y ² = 1 + d x ² y ²$ . We study the set $_{m} (a, q)$ and we parametrize it by the rational points of an algebraic curve.

Numerical characterization of nef arithmetic divisors on arithmetic surfaces

Atsushi Moriwaki (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper, we give a numerical characterization of nef arithmetic $ℝ$ -Cartier divisors of $C^{0}$ -type on an arithmetic surface. Namely an arithmetic $ℝ$ -Cartier divisor $\bar{D}$ of $C^{0}$ -type is nef if and only if $\bar{D}$ is pseudo-effective and $\hat{\deg} ({\bar{D}}^{2}) = \hat{vol} (\bar{D})$ .

Arithmetic Fujita approximation

Huayi Chen (2010)

Annales scientifiques de l'École Normale Supérieure

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We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using measures associated to $ℝ$ -filtrations.

On a certain class of arithmetic functions

Antonio M. Oller-Marcén (2017)

Mathematica Bohemica

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A homothetic arithmetic function of ratio $K$ is a function $f : ℕ \to R$ such that $f (K n) = f (n)$ for every $n \in ℕ$ . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of $f (ℕ)$ in terms of the period and the ratio of $f$ .

О числе моделей в $L_{\infty, ω_{1}}$ -теориях

Е.А. Палютин (1977)

Algebra i Logika

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Автоустойчивая 1-разрешимая модель без вычислимого семейства Скотта $\exists$ -формул

О.В. Кудинов, O. V. Kudinov, O. V. Kudinov, O. V. Kudinov (1996)

Algebra i Logika

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Сегменты рекурсивно-перечислимых $m$ -степеней.

В.В. Вьюгин (1974)

Algebra i Logika

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Displaying similar documents to “О моделях арифметики в A -изолиях.”

Displaying similar documents to “О моделях арифметики в $A$ -изолиях.”