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Shahram Mohsenipour

Publications and source records attributed to Shahram Mohsenipour.

11 recordsLinked to original sources
arXiv2023

A note on a sheaf of real regular functions

Coste and Roy in 1979 defined a structural sheaf on the real Zariski spectrum of a semi-real ring $A$ and asked whether the ring of the global sections is $\sum^{-1}_1 A$ where $\sum_1$ is the multiplicative subset $\{1+\sum_{i=1}^n a_i^2|a_i\in A, n\in N\}$ of $A$. We give a positive answer to this question for real rings and integral domains.

math.AG↗
arXiv2019

Finite sums of arithmetic progressions

We give a purely combinatorial proof for a two-fold generalization of van der Waerden-Brauer's theorem and Hindman's theorem. We also give tower bounds for a finite version of it.

math.CO↗
arXiv2019

Discrete orderings in the real spectrum

We study discrete orderings in the real spectrum of a commutative ring by defining discrete prime cones and give an algebro-geometric meaning to some kind of diophantine problems over discretely ordered rings. Also for a discretely ordered ring $M$ and a real closed field $R$ containing $M$ we prove a theorem on the distribution of the discrete orderings of $M[X_1,\dots,X_n]$ in $\Spec(R[X_1,\dots,X_n])$ in geometric terms. To be more precise, we prove that any ball $\mathbb{B}(α,r)$ in $\Spec(R[X_1,\dots,X_n]$) with center $α$ and radius $r$ (defined via Robson's metric) contains a discrete ordering of $M[X_1,\dots,X_n]$ whenever $r$ is non-infinitesimal and $α$ is away from all hyperplanes over $M$ passing through the origin.

math.LO↗
arXiv2018

On finitary Hindman's numbers

Spencer asked whether the Paris-Harrington version of the Folkman-Sanders theorem has primitive recursive upper bounds. We give a positive answer to this question.

math.CO↗
arXiv2017

On a question of Silver about gap-two cardinal transfer principles

Assuming the existence of a Mahlo cardinal, we produce a generic extension of Gödel's constructible universe $L$, in which the transfer principles $(\aleph_2, \aleph_0) \to (\aleph_3, \aleph_1)$ and $(\aleph_3, \aleph_1) \to (\aleph_2, \aleph_0)$ fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.

math.LO↗
arXiv2016

Set mappings on 4-tuples

In this paper we study set mappings on 4-tuples. We continue a previous work of Komjath and Shelah by getting new finite bounds on the size of free sets in a generic extension. This is obtained by an entirely different forcing construction. Moreover we prove a ZFC result for set mappings on 4-tuples and also as another application of our forcing construction we give a consistency result for set mappings on triples.

math.LO↗
arXiv2015

On Keisler singular-like models II

Keisler proved that if $θ$ is a strong limit cardinal and $λ$ is a singular cardinal, then the transfer relation $θ\longrightarrowλ$ holds. In a previous paper, we studied initial elementary submodels of the $λ$-like models produced in the proof of Keisler's transfer theorem when $θ$ is further assumed to be regular i.e., $θ$ is strongly inaccessible. In this paper we deal with a much more difficult situation. Some years ago Ali Enayat asked the author whether Keisler's singular-like models can have elementary end extensions. We give a positive answer to this question.

math.LO↗
arXiv2010

Model Theory of the Inaccessibility Scheme

Suppose L = {<, . . .} is any countable first order language in which < is interpreted as a linear order. Let T be any complete first order theory in the language L such that T has a kappa-like model where kappa is an inaccessible cardinal. Such T satisfies the Inaccessibility Scheme. In this paper we study model theory of the inaccessibility scheme at the level of the existence of elementary end extensions for various models of it.

math.LO↗