ﻻ يوجد ملخص باللغة العربية
It is well-known that any finite $Pi^{0}_{1}$-class of $2^{mathbb N}$ has a computable member. Then, how can we understand this in the context of reverse mathematics? In this note, we consider several very weak fragments of KH{o}nigs lemma to answer this qeustion.
We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also prove that
The classical theorem of Vizing states that every graph of maximum degree $d$ admits an edge-coloring with at most $d+1$ colors. Furthermore, as it was earlier shown by KH{o}nig, $d$ colors suffice if the graph is bipartite. We investigate the exis
We consider two combinatorial principles, ${sf{ERT}}$ and ${sf{ECT}}$. Both are easily proved in ${sf{RCA}}_0$ plus ${Sigma^0_2}$ induction. We give two proofs of ${sf{ERT}}$ in ${sf{RCA}}_0$, using different methods to eliminate the use of ${Sigma^0
This paper is devoted to Fokker-Planck and linear kinetic equations with very weak confinement corresponding to a potential with an at most logarithmic growth and no integrable stationary state. Our goal is to understand how to measure the decay rate
For (finitary) deductive systems, we formulate a signature-independent abstraction of the emph{weak excluded middle law} (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case where a qua